A study of tropical cyclone influence on the generation of internal tides

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C3, 3082, doi: /2000jc000783, 2003 A study of tropical cyclone influence on the generation of internal tides Fraser J. M. Davidson 1 and Peter E. Holloway 2 School of Geography and Oceanography, University of New South Wales, Australian Defense Force Academy, Canberra, Australia Received 4 January 2001; revised 3 September 2002; accepted 23 September 2002; published 15 March [1] An investigation is made into modifications of the semidiurnal internal tide on the Western Australian Shelf by a passing tropical cyclone. Current mooring observations are presented, taken during the passage of Tropical Cyclone Bobby (1995) over these mooring locations. The observations reveal large vertical excursions at near-inertial frequency of the isotherm during and following the cyclone s passage. This coincides with diminishing semidiurnal baroclinic tides. To gain dynamical insight into the observations, a fully threedimensional, free surface, nonlinear, hydrostatic model is applied to the Western Australian Shelf. The model is initialized with realistic stratification and forced by representative tides and cyclone winds. The wind-forcing is derived from an idealized analytical cyclone model prescribed from observed cyclone track and central pressure data, and the tidal forcing allows for the generation of internal tides. The cyclone modifies stratification by turbulent mixing, upwelling/downwelling and density advection up or down the shelf slope. This results in significant changes to internal tide characteristic paths and hence the internal tide generation process on the continental slope. Mixing is enhanced over the shelf due to shallow topography with respect to the shelf slope region creating a strong density front at the shelf edge. Observations and modeling show that the water column response to the cyclone passage is most abrupt in shallow water at 125 m, then at 300 m depth. The model reproduces the main features of the observed inertial oscillations concomitant with the dampening of M 2 internal tides after the passage of the cyclone. INDEX TERMS: 4544 Oceanography: Physical: Internal and inertial waves; 4560 Oceanography: Physical: Surface waves and tides (1255); 4219 Oceanography: General: Continental shelf processes; 4504 Oceanography: Physical: Air/sea interactions (0312); KEYWORDS: internal and inertial waves, continental shelf processes, ocean/atmosphere interactions, tsunamis and storm surges, turbulence, diffusion, mixing processes Citation: Davidson, F. J. M., and P. E. Holloway, A study of tropical cyclone influence on the generation of internal tides, J. Geophys. Res., 108(C3), 3082, doi: /2000jc000783, Introduction [2] The Western Australian Shelf features strong internal tides, particularly during the summer when the shelf is well stratified [Holloway et al., 2001; Holloway, 1988]. This 200 km wide shelf harbors several offshore oil and gas operations which are sensitive to strong currents generated by internal tides. Further challenges to offshore operations are tropical cyclones that pass through the region annually between January and March. This paper focuses on the changes in shelf circulation and water stratification during the passage of 1 Now at Fisheries and Oceans, St. John s, Newfoundland, Canada. 2 It was an immense privilege and a wonderful experience to have learned from and worked with Peter as a postdoc at the School of Geography and Oceanography in Canberra. He will be remembered as the kindest and most respectful scientist possible, all the while striving humbly for excellence with a sense of humor. Peter Holloway died 27 October 2002 in Canberra and will be dearly missed by all. Copyright 2003 by the American Geophysical Union /03/2000JC a tropical cyclone over a tidally active coastal ocean. Specifically, we are interested in the effect of extreme winds in modifying the generation and propagation of an internal tide and on the generation of near inertial period motion. [3] Internal tide modeling studies usually involve forcing the lateral open boundaries with a prescribed barotropic sinusoidal tidal elevation. Generation of the internal tide comes from the interaction of the barotropic tide with bottom topography. Strongest generation occurs when stratification dictates that the slope of internal wave characteristics at tidal frequencies are close to parallel to in situ bottom slope. This generates waves near the critical bottom slope that travel along characteristics. The bottom boundary layer can be a region of intensification of currents from internal wave as well as a region of asymmetry between upslope and downslope flow [Holloway and Barnes, 1998]. [4] Tropical cyclones, hurricanes, and typhoons are characterized by a slowly moving atmospheric depression that forms over the ocean, generating intense winds. The curl and divergence of wind stress associated with the cyclone 27-1

2 27-2 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES depress the sea level beneath it and in its wake [Geisler, 1970; Hearn and Holloway, 1990]. This depression, by geostrophy, generates strong clockwise flow through the entire water column [Shay et al., 1990]. Furthermore, the cyclone accelerates fluid in opposite directions to each side of the cyclone. This generates counterclockwise oscillatory currents at near-inertial frequencies, with a 180 phase difference on opposite sides of the cyclone track. Consequently, this secondary near-inertial oscillating flow creates alternating convergence and divergence zones in the wake of the cyclone [Shay and Chang, 1997], allowing for the meandering of the cyclonic flow pattern around the surface depression created in the cyclone s wake. [5] Nonlinear terms play an important role in the ocean s response to a cyclone. Greatbatch [1983] and Shay et al. [1990] show that cross-track advection of heat and momentum lead to a maximum response of current and temperature to the left/right of the cyclone wake (Southern/Northern Hemisphere). Along-track advection of momentum generates a rapid transition from a downwelling phase below the cyclone to an upwelling phase, which is then followed by a slower transition to a downwelling phase [Greatbatch, 1983]. [6] In addition to local processes, wind forcing by cyclones in coastal areas may generate coastal trapped waves, particularly continental shelf waves that impacts downstream in the sense of wave propagation (north to south along the west coast of Australia) [Tang et al., 1997]. [7] Tropical cyclones have an impact on the stratification in the ocean, imparting momentum to the upper ocean and thus enhancing mixing. Ocean stratification can also affect a passing cyclone with features such as warm or cold core rings which can increase or decrease cyclone strength [Hong et al., 2000]. Internal tides can affect the surface temperature field, particularly at shelf breaks [Le Tareau and Mazé, 1993] owing to the spatial distribution of intense currents caused by strong near-surface flow. This induces vertical mixing, thereby reducing surface temperature. Strong wind forcing can modify these internal tide-induced surface temperature signatures. [8] In this paper we investigate the influence of a tropical cyclone on the internal wave field on the Western Australian Shelf using the three-dimensional (3-D) nonlinear primitive equation Princeton Ocean Model (POM) [Blumberg and Mellor, 1987] with realistic stratification, bottom topography, tidal and wind forcing. The cyclone is prescribed, and there is no atmosphere-ocean feedback. We focus on the cyclone s impact on water column stratification through vertical mixing and upwelling/downwelling and on how these processes affect the generation of strong near-inertial motion and the propagation and generation of the internal tides. The work focuses on a shelf break region where sloping topography and stratification are important and where internal tide generation takes place. This differs from previous studies of open-ocean response to cyclones and to response over inner shelves and bays where internal tide activity has been neglected or tends to be weak. 2. Observations 2.1. Mooring Data [9] Two moorings (M2, M4: Figure 1) provided data at several depths during the passage of Tropical Cyclone Bobby. Mooring M2 was situated in 300 m of water with six S4 electromagnetic current meters recording velocity and temperature at 40, 90, 140, 190, 240, and 300 m depths. Mooring M4, located in 125 m of water and composed of five acoustic current meters placed at 12, 39, 66, 99, and 120 m depths, measured currents and temperature. However, the current meter at 99 m depth malfunctioned and only recorded temperature. Here we focus on data collected from Julian day 46 to 64, a section of the data that has not previously been published or analyzed. The internal tidal structure is discussed by Holloway et al. [2001] who analyzed the first 30 days of mooring data prior to the advent of cyclone Bobby. [10] Tropical Cyclone Bobby formed in the East Timor Sea north of Darwin and was named on 22 February The cyclone followed a track parallel to the coastline, roughly 200 km offshore (Figure 1), intensifying to a severe tropical cyclone (mean winds > 32 m s 1 ) on 22 February. It passed directly over mooring M2 in the evening of 23 February (day 54), after which the cyclone intensified with mean winds up to 50 m s 1 and veered inland ultimately decaying into a tropical rain bearing depression over Western Australia [Bureau of Meteorology, 1995] Wind Data [11] To model wind speeds over the mooring locations at the ocean-air interface we use the analytical formulation of Holland [1980] for cyclone wind distribution. The azimuthal wind speed for a cyclone is given by n h i o 0:5 vr ðþ¼ br ð m =rþ b ðp n P c Þ:* exp ðr m =rþ b =r a þ r 2 f 2 =4 rj f j=2; where b =1.5+(980 P c )/120 is a form factor, P c is the cyclone central pressure, P n is the environmental pressure, r is the distance from the center of the cyclone, r a is atmospheric density set at 1.34 kg m 3, f is the Coriolis parameter set at s 1, and r m is the radius to maximum wind intensity. We apply no cyclone-induced atmospheric pressure forcing to the ocean mode, only wind stress forcing. Azimuthal wind speed is then converted to azimuthal wind stress using [Smith and Banke, 1975; Frank, 1984] tðþ¼ 1:25C r d vr ðþ 2 C d ¼ ð0:63 þ 0:0633 * vr ðþþ*0:001 if vðþ< r 25ms 1 C d ¼ ð2:28 þ 0:033 * ðvr ðþ 25ÞÞ*0:001 if vðþ> r 25ms 1 : ð4þ Here t(r) is azimuthal wind stress which is separated into x and y components when applied to the model. [12] The above cyclone model used is a simplification of the complete Holland model which provides asymmetric wind forcing. Owing to uncertainty in observed cyclone parameters (track and central pressure), we choose to use the simplest cyclone model. At the North Rankin platform, located near mooring M4 (Figure 1), the model predictions of peak wind speeds exceed the observed values by a factor of approximately two. Uncertainty in the track of a cyclone, ð1þ ð2þ ð3þ

3 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES 27-3 Figure 1. Topography of the Western Australian Shelf showing locations of the moorings M2 and M4. The black line represents Tropical Cyclone Bobby s track as reported by the Australian Bureau of Meteorology (ABM). Open circles mark the position of the cyclone s eye every 3 hours. The top left inset graph shows maximum calculated wind stress of Cyclone Bobby based on ABM data (equations (5) (8) with reduced wind speed, as discussed in the text). The asterisks correspond to marked cyclone track positions on the main figure. The inset map shows the complete track of Tropical Cyclone Bobby with dots indicating the location at 2 day intervals. For reference with other plots, note that 23 February is Julian day 54. central pressure, and radius to maximum winds makes it difficult to simulate the exact forcing of the ocean at any specific location. This is particularly true when the cyclone is intense with a small radius to maximum winds, and differences of 1 2 km in position can have dramatic different wind stress levels 40 km from the eye of the cyclone. Furthermore, there is no data to validate or constrain the form factor b in equation (1) for cyclone Bobby. This mainly affects the tapering off of winds beyond the radius of maximum winds. To compensate for the difference between model and observed winds at North Rankin, we reduce our modeled wind speeds by 20%. This has the effect of reducing wind stress by 64% for winds less than 25 ms 1 and by 50% for winds greater than 25 ms 1. Maximum modeled wind stress (including the 20% reduction) is shown in the inset on Figure 1. While there remains a level of uncertainty in the model wind field, this study focuses on establishing the basic characteristics of the response of shelf waters to Tropical Cyclone Bobby Observation Results [13] Initially, the strong tidal flows are removed from current meter records by low-pass filtering to examine the cyclone-forced motions. Figure 2 shows the 24 hour lowpass filtered total currents observed at mooring M2 and M4. Also shown is the computed wind from the Australian Bureau of Meteorology storm tracks at each of the moorings using equation (1), including the 20% reduction as discussed above. In addition, for mooring M4, observed wind from the North Rankin Platform (5 km distant) is shown. [14] The cyclone passes almost directly over the mooring M2 at around 10 pm on day 54 and is about 40 km from M4 at this time. This is also the closest approach of the cyclone to mooring M4. Winds differ at the M2 and M4 mooring locations owing to the short spatial scale of the cyclone. Figure 2 shows that observed and computed winds at M4 agree qualitatively, although they differ slightly in strength. Possible sheltering effects of the North Rankin platform on the observed winds are thought to be minimal. Prior to the arrival of the cyclone, computed winds at the M2 site of 40 m/s are directed off-shore. As the cyclone passes over the mooring, the winds die down and resume 8 hours later, this time weaker and directed 45 degrees northward of the onshore direction. The storm moved with an average speed of 7.5 km hr 1 (2.1 ms 1 ) in the vicinity of mooring M4. As the cyclone approaches the M2 mooring site, low-pass

4 27-4 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES Figure 2. (a) Vector plot of computed winds at mooring 2 (M2) due to Tropical Cyclone Bobby and the observed low pass (24 hour) filtered velocities at six depths for M2 situated in 300 m of water. Note that model winds have been reduced by 20% as discussed in the text. The axis are rotated 45 clockwise from north to line up with the shore line. (b) As in Figure 2a but for Mooring 4 situated in 125 m of water. filtered velocity magnitudes increase to 80 cm s 1 in the upper water column (40 m depth). Velocity direction reverses for 12 hours as of day 55. This coincides within 3 hours of the winds resuming over mooring M2 with an on-shore direction. Following the reversal of currents, for the remaining 8 days of the observations, currents are directed southward and parallel to the shore. This phenomenon is observed at all depths down to 190 m. At 240 and 290 m depths the impact of the cyclone is minimal, with currents slightly stronger on day 55. Here there appears to be no predominant southward shore-parallel flow as is observed closer to the surface. [15] Prior to the cyclone, currents at 90 m (20 cm s 1 )are twice as strong as observed at 140 m of depth. During and following the cyclone, however, observed currents at 90 m and 140 m are equally strong. Furthermore, strong southward shore parallel velocities at M2 characterize the upper 190 m of the water column. [16] Observed currents at the shallower M4 mooring (125 m depth) are shown at 12, 39, 66, and 120 m. Velocities reach 80 cm s 1 on day 55 near the surface (12 m). After the cyclone passage, velocities drop, within 2 days, to about 20 cm s 1. A similar yet weaker pattern is observed at 40 m. This contrasts with current speeds observed at 40 m at mooring M2 where currents remain comparatively strong for the week following the passage of the cyclone. [17] The effect of the cyclone on subtidal frequency currents is visible down to 5 m above the sea floor at mooring M4. Strong along-shore currents are observed during and immediately following the passage of the cyclone from day 54 to day 56 at 66 m and 120 m depths. However, at 120 m and 66 m depth, water velocities drop off to levels observed prior to the arrival of the cyclone at day 57. At 120 m, near-inertial oscillations dominate the current time series with strong northward and along-shore mean flow, except during the passage of the cyclone. [18] The strong currents appearing during the cyclone at M4 near the bottom (125 m of water) are rapidly damped compared with near-surface flows, and this may be attributable to bottom friction. Furthermore, while overall peak currents due to the cyclone are stronger at mooring M4 than at mooring M2, they drop off more rapidly. [19] The density stratification in Figure 3 was computed by taking the 4 day average of the vertical temperature profile prior to and following the cyclone. Temperatures were then converted to density, assuming a constant salinity of 35.5 psu, as salinity variations make only a small contribution to density variations in this region. The passage of the cyclone decreases vertical stratification in the top 90 m of the water column at mooring M2 and in the top 60 m of the water column at M4. There is also a small decrease in stratification from 90 m to the bottom (125 m) at mooring M4. The influence of Tropical Cyclone Bobby on observed velocity reaches the bottom at mooring M4 but does not reach to the bottom of mooring M2 (290 m). At mooring M2 the vertically averaged density increases dur-

5 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES 27-5 raising isotherms by 25 to 75 m which then relax, generating near-inertial oscillations of up to 20 m amplitude. This finding is consistent, for example, with the theoretical work of Shay and Chang [1997] and Shay et al. [1990]. The initial upwelling surge produced by the cyclone is visible throughout the water column but is more spread out in time near the surface where the ensuing near-inertial oscillations are not as prevalent as at depth. In addition, following the cyclone s passage, there is an 11 hr delay in the isotherm crest near the surface relative to the corresponding crest near the bottom. The surface layers above about 70 m become less stratified after the cyclone, seen by an increase in spacing between isotherms (Figure 4). However, after about 6 days the initial stratification reestablishes. This rapid response suggests advective processes are important in reestablishing the density field, rather than surface heating which would be expected to take significantly longer. At M2 however, below 100 m, isotherms remain raised by m above precyclone levels for the remainder of the observation period, indicating that readjustment at depth may take more time. [22] Previous work has shown that near-inertial oscillations generated by a cyclone tend to be at frequencies Figure 3. Observed density stratification (computed from temperature observations) for 4 days (Day 50 54) prior to cyclone Bobby (thick line) and for 4 days following the passage of the cyclone (Day 56 60) (thin line) for moorings M2 and M4. ing the cyclone s passage, which is indicative of upwelling or could also be associated with surface cooling from the cyclone. [20] The cyclone-induced stratification changes modify the vertical modal structure of the internal tide. However, modal analysis using the density profile computed in Figure 3 indicates that the cyclone has little influence on the 1st normal mode and a small influence on the second normal mode which is more sensitive to stratification. At M2 the baroclinic first mode wave speed decreases by 6% from an initial value of 1.23 m s 1 and the second mode wave speed decreases by 15% from a value of 0.68 m s 1. The cyclone has a greater influence on the internal modes at mooring M4 than at mooring M2 with phase speeds of the first/second baroclinic modes decreasing by 7/20% from initial values of 0.57/0.30 m s 1, respectively Near-Inertial Response [21],The near-inertial response of stratification at moorings M2 and M4 from Tropical Cyclone Bobby is evident in Figure 4 from 24 hour low-pass filtered temperature contours. The inertial periods at moorings M2 ( N) and M4 ( N) are and hours, respectively. The figure shows weak near-inertial oscillations of the thermocline at both moorings prior to the cyclone s passage with amplitudes ranging from 5 m to a maximum of 12 m at middepth (150 m). At M2, a first observed effect of the cyclone is a dip (lowering) in the isotherms by m at middepths and below. This is followed by a sudden impulse Figure 4. (a b) Contour of observed 24 hour low pass filtered temperatures showing inertial oscillations at moorings M2 and M4. Temperatures at M2 were recorded at 40, 90, 140, 190, 250, and 290 m depths. For M4 observation depths were 12, 39, 66, 99, and 120 m. Temperature intervals are 1 C. The thick contour represents the 20 C isotherm for M2 and the 24 C isotherm for M4. (c) Amplitude of inertial period demodulation (36hrs) of the 19 C isotherm at M4 (dark line) and of the 25 C isotherm at M2 (gray line).

6 27-6 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES has been advected upslope. Figure 4 also shows the demodulated inertial period amplitudes of the 25 C (M2) and 19 C (M4) isotherms. These show the large increase in amplitude of near-inertial motion at the start of the cyclone s impact with a slow decay over 4 to 5 days after the cyclone s passage. Figure 5. As in Figure 4 but using bandpass filtered data between 4 hours and 24 hours to show semidiurnal tidal oscillations. Here temperature intervals are 2 C. The thick contour represents the 20 and 24 C contour for M2 and M4 moorings, respectively. The Bottom panel shows demodulation amplitudes at the M 2 tidal period for the 19 (25) C isotherm at the M2 (M4) mooring shown by the dark (gray) line. slightly greater than f [Shay and Chang, 1997; Greatbatch, 1983]. Our observations corroborate these previous findings at both the M2 and M4 sites. At mooring M4, averaging over three inertial oscillations following the cyclone passage yields a near-inertial period of 35.2 hours and a frequency of 1.02 f. At M2, the same calculation reveals a near inertial frequency of 1.28 f at depth ( m). [23] At mooring M4, the isotherm response to Tropical Cyclone Bobby is qualitatively similar to that at M2 (Figure 4) despite the mooring being located in shallower water (125 m) and 40 km further away from the cyclone track. However, the large initial downwelling dip and subsequent upwelling phases (day 55, Figure 4) are sharper and more abrupt than seen at M2. There is a net increase in stratification in the lower half of the water column, while there is a net decrease in stratification in the upper half after the cyclone. From their positions prior to the cyclone, isotherms are generally raised following the cyclone at M2, where as at M4 the isotherms are lowered, once the upwelling phase is over. Near the bottom, at M4 (100 m), near-inertial thermocline oscillations are strong and persistent with peak to peak heights of about 15 m. Cold bottom water intrudes momentarily in the observations during the passage of the cyclone at M4 and is most likely deeper offshore water that 2.5. Tidal Period Response [24] We now analyze 4 24 hour band pass filtered time series of temperatures at M2 and M4 (Figure 5) to look at the cyclone s effect on the semidiurnal internal tide. Initially, semidiurnal internal tidal amplitudes range from 15 to 32 m. The amplitude of the tidal oscillations increase by 25% over the few days leading up to the cyclone s passage with a maximum oscillation at middepth of over 50 m. The oscillations are approximately in phase over the entire depth. Following the cyclone, isotherm displacement amplitude is dramatically reduced, particularly at mooring M4. [25] Our temperature observations corroborate previous understanding of an ocean response to a passing cyclone. The thermocline is suddenly raised underneath the cyclone, principally by surface divergence. As the cyclone moves away, the thermocline subsides concomitant with the generation of near-inertial oscillations created by the barotropic near-inertial oscillations that cause alternating convergence and divergence of flow in the surface through of the cyclone s wake. From our observations in coastal waters with water depths comparable to the mixing depth of momentum induced by the cyclone, bottom topography plays a significant role in modifying the circulation response to the cyclone. The difference here with previous work is that our data was collected on a shelf/slope region and not in the deep ocean. Furthermore, we have illustrated the effect of the cyclone on the internal tide. [26] Note that the neap tide occurs on day 56, such that barotropic tidal oscillations are at the minimum of the 15 day cycle two days after the main impact of the cyclone. However, the internal tide is not necessarily phase locked to the barotropic tide in this region Holloway [1984], so large internal tides can occur at neap astronomical tide. Hence the observed increase in the internal tide toward day 54, when the cyclone crosses the moorings, is consistent with internal tide dynamics in this region. The passing cyclone clearly damps the internal tidal oscillations for 4 6 days after its passage, particularly at the shallow mooring M4. 3. Model 3.1. Model Description [27] We use the 3-D, nonlinear, free surface hydrostatic Princeton Ocean Model (POM) [Mellor, 1992] to model the combined effects of cyclone and tidal forcing. This model solves the primitive equations on a sigma (terrainfollowing) coordinate system with vertical mixing modeled by a Mellor-Yamada level 2.5 turbulence closure scheme [Mellor and Yamada, 1974]. The model domain is shown in Figure 6. A horizontal resolution of 8 km is used and is sufficient to resolve the first baroclinic mode in waters deeper than 40 m. The model comprises 24 vertical sigma levels, with vertical resolution concentrated in the surface and bottom layers. Initial stratification is horizontally uniform and taken from observations in January 1995 on the

7 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES 27-7 relaxation constant which varies between values of 1 at the boundary and 0, 10 gridpoints in from the boundary. The local solution (f o e (t)) comprises the linear addition of prescribed tidal elevation and a local linear wind driven solution which is the solution ðudþ ¼ fvd t bx þ t sx ¼ t by þ t sy : Figure 6. Model topography and cyclone tracks. (a) Idealized cyclone with a coast parallel track at Y = 350 km. (b) Track for cyclone Bobby as derived from the Australian Bureau of Meteorology storm tracks. Western Australian Shelf and is identical to that of [Holloway, 2001]. [28] Open boundary conditions in the model take into account both space and time variable wind forcing as well as barotropic M 2 and S 2 tidal forcing and are based on work by Palma and Matano [1988, 2000] who, in a comparison of model boundary conditions for POM, identify an optimum set of open boundary equations for time and spatially dependent wind forcing. The set of boundary equations we use is identified as the MOA set (Palma and Matano [1988]) and consists of a combination of a relaxation scheme for the 2-D barotropic equations, an implicit Orlanski radiation condition on 3-D horizontal velocities, and a relaxation/advection scheme for inflow/outflow on tracer variables of temperature and salinity. [29] For the boundaries of the 2-D barotropic (external) component of the model we use a flow relaxation scheme where surface elevation and barotropic velocities are relaxed to a local solution at the boundaries [Martinsen and Engedahl, 1987; Roed and Smedstand, 1984] f e ¼ af e oðþþ t ð 1 a Þfe : ð5þ Here f e is depth-averaged velocity or surface elevation computed by the POM model, f o e (t) is the value of the variable prescribed by the local time-dependent solution at the boundary, and a = 1 tanh[0.3(i i o )] is the Here U and V are the 2-D barotropic velocities in the x and y directions, respectively, D is total water column depth (H + h), h is the surface elevation, f is the Coriolis parameter set at s 1, t bx (t by ) are bottom stress in the x(y) direction and t sx (t sy ) is surface wind stress in the x(y) direction. Normal gradients in bottom topography with inflow relaxation boundary zones (10 grid points) are removed. [30] The above local model allows for the propagation of surface gravity waves parallel to the open boundary but not perpendicular to it [Palma and Matano, 2000]. The local model is solved over a swath 10 grid points deep, parallel to the open boundary. The eastern and western open boundaries intersect with the northern open boundary, unlike Palma and Matano [2000] where the northern boundary was closed. We make the assumption here that waves cannot propagate around corners from one open boundary (i.e., east) to the next (i.e., north). We thus implement a radiation condition at the open boundaries to permit waves to exit the local model boundary solution domain. Furthermore, in order to prevent continuous growth in sea surface elevation near the coast, we add a linear damping term (implicitly) of 5 days to the local wind driven model equations. [31] To the above local solution for velocity and surface elevation, we add a prescribed time varying tidal elevation from the linear superposition of M 2 and S 2 tidal elevations (depending on model runs). Tidal constituent information is obtained by interpolating to our domain boundaries tidal constituent amplitude and phase information from a 0.5 resolution global tidal model FES [Le Provost et al., 1998]). The model domain is a sub region of that used by Holloway [2001], where detailed comparisons are presented between observed and modeled barotropic tides. No tidal forcing is added to the local solution of velocities. [32] The boundary relaxation scheme (equation (5)) applied to the local tidal solution induces a 4.6 hour lag when compared both with tide gauge observations and a model run where boundary elevations are clamped directly to prescribed tidal elevations (as given by Holloway [2001]). We correct for this delay by adjusting the phase of the tidal forcing. For the 3-D internal mode an implicit Orlanski radiation scheme is applied to baroclinic velocities [Orlanski, 1976; Chapman, 1985]. For salinity and temperature inflow into the domain, the relaxation scheme is applied to initial temperature and salinity stratification values. On outflow, an advection scheme is used [Mellor,

8 27-8 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES Table 1. List of Model Runs a Runs Cyclone Tides run 1 M 2 run 2 TC1 M 2 run 3 TC2 M 2 run 4 TC3 M 2 run 5 TC4 M 2 run 6 TC Bobby M 2 +S 2 a Descriptive list of model runs performed, including forcing components for model. TC1, TC2, and TC3 are idealized cyclones with a straight shore parallel path at y = 200, 350, and 500 km with a constant translation speed of 3 m s 1, constant central and environmental pressure and a fixed radius to maximum speeds of 50 km. Tropical Cyclone Bobby is a cyclone whose time-dependent central pressure and position are prescribed from cyclone track observations by the Australian Bureau of Meteorology. M 2 refers to forcing by the M 2 semidiurnal tide. In this case the amplitude of the M 2 tide is taken from the addition of the M 2 and S 2 tidal amplitudes to simulate the strongest possible M 2 tide (i.e., the spring neap tide). M 2 +S 2 refer to forcing by both the M 2 and S 2 barotropic tide at the boundary. 1992]. In addition, within 10 grid points of the open boundaries, the horizontal diffusion and viscosity coefficients are increased to 500 m 2 s 1 to remove any spurious instabilities from the boundary Model Runs [33] The model is initialized at rest with horizontally uniform summer stratification. Model wind and tidal forcing is gradually ramped up over a 1 day period to avoid spurious waves due to model spin-up. Parameters used in the various model runs are presented in Table 1. Model runs were integrated for 18 days, allowing the cyclone to start from 1000 km outside the model domain and move through the whole domain and out the other side. Runs discussed below consisted of a tidal forcing only case, cases with idealized cyclone tracks, and a realistic run of Tropical Cyclone Bobby Idealized Cyclones [34] We first test the response of the internal tide to idealized cyclones with various shore parallel tracks and one with a cross-shelf track (Figure 6, Table 1). We analyze the response of the water column at cross-section C1 (Figure 6) for these various cyclone tracks and compare with a model run using only tidal forcing. [35] Daily averaged temperature stratification sections 2 days prior, the day of, and 2 days following the passage of the cyclone are shown in Figure 7. The stratification in the case of tidal forcing only (run 1) shows some variability associated with the internal tide but is essentially steady throughout this period. The passage of the near-shore cyclone influences the shelf region by enhancing mixing and by creating surface divergent currents over the shelf. Below 100 m depth along the slope bottom there is upwelling. The shallow part of the shelf becomes well mixed. A Figure 7. Cross section of temperature stratification for idealized cyclone runs 1 5 (Table 1).

9 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES 27-9 Figure 8. As in Figure 7 but for M 2 tidal amplitude of cross shore baroclinic flow. strong bottom temperature gradient at the top of the shelf break (Y = 250 km) in m of water divides the wellmixed shelf water from stratified water beyond the shelf break. Horizontal flow divergence beneath the cyclone produces strong upwelling as seen in models over the open ocean. Intense mixing over the shelf underneath the cyclone erodes stratification preferentially over the relatively shallow shelf but not over deeper water. This combination of upwelling and strong vertical mixing produces the strong temperature front near the upper edge of the shelf break. As the cyclone track is moved further offshore (runs 3 and 4), the shelf and slope water near bottom temperature differences drop from 18 C to about 7 C. [36] Another feature caused by the link between mixing and stratification (in the near shore cyclone run) is the local maximum in the near-surface isotherm height 350 km offshore. This results from reduced vertical mixing due to increased stratification from upwelling between 250 and 350 km offshore. However beyond 350 km, vertical mixing is slightly increased at the location where cyclone winds are still relatively strong and the stratification weaker. This location of increased mixing causes a minimum in surface temperature. [37] For the cross-shore cyclone case (run 5) where the cyclone track is 50 km to the north (upstream) and parallel to cross section C1, modeled isotherms show first downwelling at the shelf slope (day 7) before water is upwelled onto the shelf after the cyclone passage (day 9). The tongue of upwelled near-bottom water on the shelf gradually thins out and recedes down the shelf slope over the course of this model run (another 6 days). In run 5 the water is well mixed over the shelf, with an intrusion of colder water near the seabed on the outer part of the shelf (Figure 7). Away from the shelf slope, there is a depression in isotherms centered around Y = 350 km. [38] The presence of the continental slope impacts on the stratification response to a passing cyclone. As an example, in run 3, the slope of the isotherms are steep on the shelf side of the track (Y < 350 km) compared with the off-shore side of the cyclone track (Y > 350 km). [39] The three ways in which the cyclone can modify stratification are by upwelling and downwelling due to surface divergence and convergence, increased mixing due to strong vertically-sheared currents, and advection of density up or down the slope. These changes in stratification vary the slope of the characteristics for internal waves w defined as 2 f 1=2. 2 N 2 w The slope of these characteristics relative to the slope 2 of the seabed is an important parameter in determining the generation of internal tides [Baines, 1982]. Strongest generation can be expected for critical slopes where the seabed and characteristics are parallel. Hence varying stratification in response to a tropical cyclone can moderate internal tide generation and propagation.

10 27-10 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES Figure 9. As in Figure 7 but for M 2 tidal amplitude of vertical displacement. [40] We examine the change in the amplitude of crossshore baroclinic velocity of the M 2 tidal constituent for cross section C1. The baroclinic velocity is defined as the difference between total velocity and the depth-averaged value. First, we focus on the response in the top 300 m of the water column. For tidal forcing only, a quasi-steady state is reached showing strong cross-shore baroclinic current at the M 2 tidal frequency centered above the shelf break (Figure 8). Near the bottom on the shelf there is a thin layer of strong baroclinic tidal currents (20 cm s 1 ). This internal tide is significantly modified by the different cyclones. [41] Of the four idealized cyclone runs, the inshore track (run 2) quells the M 2 baroclinic velocities the most, with amplitudes only significant along the bottom at the shelf break. Two days prior to the arrival of the cyclone in this run, the baroclinic velocities are reduced. This appears to be in response to weak upwelling close to the seabed (Figure 7) induced by the broad cyclone wind field that extends well beyond the radius to maximum winds. Two days after the cyclone there is little baroclinic tidal current except near the surface over deeper water. For the midshore cyclone track (run 3), tidal velocities are damped mostly during and after the passage of the cyclone. As in run 2 at day 9 (2 days after cyclone s passage), the strong bottom-intensified M 2 baroclinic tidal currents centered around 150 m depth seen in the tides-only forced run are absent. There are some strong tidal period currents sparsely distributed offshore. In the case of the offshore cyclone track (run 4), the model shows an overall strengthening of baroclinic tidal currents near the bottom above the shelf break with a movement offshore by 50 km of the main generation site. There is little baroclinic tidal current on the shelf. The cross-shore cyclone track run (run 5) produces the strongest cross-shore baroclinic tidal flow amplitude. Two days following the cyclone passage, amplitudes of 20 cm s 1 are found deep along the shelf break (i.e., 200 m). [42] Figure 9 shows the vertical displacement amplitude at the M 2 tidal frequency throughout the passage of the cyclone for the top 300 m of the water column. As seen in the tidal velocity plots, the inshore cyclone track weakens the internal tide while the offshore track strengthens the internal tide. The presence of the cyclone does not change the location of maximum vertical displacement but changes the intensity of it. The vertical displacement under the offshore parallel cyclone track is also enhanced with respect to the tidal forcing only case over the shelf break. [43] The cross-shore cyclone produces an energetic response of M 2 tidal displacements prior to, during, and following the cyclone s passage. Prior to the cyclone s passage, the elevation amplitude is enhanced along the upper shelf slope ( m depth) as well as offshore (Y = 400 km). During the cyclone the tidal amplitude is damped above 150 m depth but enhanced below this depth. Following the cyclone passage, the internal tidal elevations

11 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES Figure 10. Amplitude of M 2 vertical displacement as in Figure 9 but over a greater depth scale. The dotted lines are characteristics calculated from the density field in Figure 7. are intense above the shelf at Y = 350 km with displacement amplitudes above 30 m. This patch of intense internal waves is also 50 km further offshore than in the tide-only case (presumably owing to change in internal wave characteristics). The observed pattern coincides with the changing stratification on the shelf due to the cyclone, with downwelling at the shelf slope during the cyclone passage and upwelling pursuant to it. [44] The cyclones have an influence on internal tides over the entire water column down to 2000 m or more as shown in Figure 10 for the vertical M 2 tidal displacement. Where internal wave characteristics (plotted) are parallel to bottom topography there appears to be generation of internal waves. Figure 11 demonstrates that the various cyclone tracks have a significant impact on the ratio of bottom slope over characteristic slopes with respect to the critical value. Owing to the spatial variability of the internal tide with different forcing scenarios, it is hard to relate at a fixed site, whether critical bottom slope produces the strong internal tide observed in Figures 8, 9, and 10. For internal tide amplification, bottom slope needs to be near critical over a length scale of a baroclinic wavelength. The cyclone passage does have a strong effect on the internal tide at depth, particularly for runs 4 and 5 (offshore shore-parallel and cross-shore cyclone track). The effect, however, is greatest in the cross-shore cyclone model run. Figure 11. Vertical profile of ratio (s) of bottom slope over characteristic slope calculated from daily average density profile at Y = 280 (a) and 400 km (b) along crosssection C1 two days following the passage of the cyclone in idealized model runs 1, 2, 4, and 5.

12 27-12 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES Figure 12. Modeled temperature stratification for run 6 with a realistic representation of Tropical Cyclone Bobby and forcing with the M 2 and S 2 tidal components (to be compared with Figures 4 and 5). No filtering was applied to the model output. Contour intervals are 2 C, with the thick line representing 20(24) C for M2(M4). [45] Internal tide production is acknowledged to be spatially highly variable on the Western Australian Shelf [Holloway, 2001]. Additional cross-sections examined in the model (not shown) show that weak internal cross-shelf tidal flow in run 1 (base case) can be amplified (rather than damped) under inshore cyclone tracks. The important factor is the path of the cyclone with respect to the location of the generation of internal tides on the shelf. If a cyclone passes over an area of internal tide generation the signal is usually damped owing to modification in stratification. However, if the cyclone track passes offshore away from the tidal generation area, the internal tides tend to be enhanced. In general, the vertical M 2 tidal displacement amplitude seems to strengthen due to the passage of an offshore cyclone and is diminished only in the inshore cyclone case Tropical Cyclone Bobby [46] The model is run using wind forcing representative for Cyclone Bobby [Bureau of Meteorology, 1995] (Figure 6) in addition to M 2 and S 2 tidal forcing. Here horizontal resolution is increased from 8 to 4 km. Higher resolution permits better representation of the internal tide particularly in shallower water where baroclinic wave lengths are shorter. The net effect of increasing model resolution is a better match with observations and a strengthening of internal tidal amplitudes by up to a factor of two. The inertial and tidal response of water column stratification at moorings M2 and M4 are shown in Figure 12 and can be compared with observations in Figures 4 and 5. Prior to the cyclone s passage, the modeled isotherms show tidal oscillations only and no inertial oscillations. The observations, however, show weak inertial variability with amplitudes less than 5 m, attributable to noncyclone wind forcing not included in the model. As the cyclone passes over the mooring, model results show an initial dip in the isotherms of up to 50 m before an upwelling phase where the isotherms are raised by as much as 150 m (mooring M2). Subsequently, the modeled isotherms relax with about 3 4 inertial oscillations, depending on depth. The model shows that the inertial oscillations persist longer and are more pronounced at depth than near the surface, in agreement with the observations. [47] At mooring M4, model results are similar to observations with a downward dip of 50 m before a strong and sharp isotherm rise of up to 90 m. This rapid response to the cyclone is then followed by inertial oscillations that are

13 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES Figure 13. Observed (gray) and modeled (black) crossshore barotropic (depth-averaged) currents at moorings M2 (top) and M4 (bottom). strongest near the bottom. The model reproduces the observed distinct near-inertial oscillations of isotherms near the bottom at M4. Observed isotherms start to relax towards initial depths by the second inertial oscillation. However, in the model the first inertial oscillation raises isotherms above the height of the initial upwelling response to the cyclone. In general, the modeled inertial response is larger than observed. This may be an indication that applied wind stress in the model is overestimated and that the wind field model produces too much surface divergence in the ocean. The model reproduces the strong sharp upwelling response at mooring M4 in 120 m of water and the more gradual upwelling response at mooring M2 in 300 m of water (Figure 12). [48] The model (Figure 12) shows a slight strengthening of tidal oscillations of isotherms prior to the cyclone s arrival (despite the near neap tide conditions) as observed (Figure 5). This is most likely in response to changing background stratification in response to the cyclone, as demonstrated in the idealized model runs. The patterns of modeled internal tidal displacement closely follow those observed, although model tidal oscillations are slightly weaker than observed. Also, the upwelling inertial impulse produced by the cyclone is slightly more pronounced in the model than observed. [49] A pattern visible in both the model and the observations is the dominance of tidal oscillations over inertial oscillations, prior to the arrival of the cyclone and the dominance of inertial oscillations pursuant to the cyclone s passage (Figures 12 and 5). This pattern is most noticeable at mooring site M4. Observations also contain oscillations at a 6 hour period which is only slightly apparent in the model. No M 4 tidal forcing is specified at the boundaries but harmonics of the M 2 tide could produce such signals. [50] A comparison of modeled cross-shore barotropic (depth-averaged) velocity and its observed equivalent is shown in Figure 13. Agreement is good for both the cyclone-driven flows and barotropic tidal oscillations. For the along-shore barotropic flow (not shown), the model reproduces the weak tidal oscillations that are observed. While the response to the cyclone agrees with observations, the strength of the modeled along-shore current response is greater by a factor of 2 3 during the initial response to the cyclone. This is most likely due to uncertainties in the modeled wind field. Just prior to the arrival of the cyclone, modeled cross-shore depth-averaged velocity tidal oscillations diminish more than in the observed case consistent with the approach to neap tides at this time. [51] Modeled and observed baroclinic currents (total minus depth-averaged values) are presented in Figure 14 for the cross-shelf component. Model and observed crossshore baroclinic tidal velocity oscillations do not increase in amplitude prior to the cyclone passage, as seen with modeled and observed isotherm and M2 tidal displacements (Figures 4 and 12). The model reproduces the observed sequential pattern of response during and following the cyclone s passage with initial increased offshore flow, strong onshore flow, and several inertial oscillations of the current followed by resumption of steady tidal oscillations. Near the surface at M2 the model reproduces the baroclinic inertial response to the cyclone. The internal tide current oscillations in the model are at least 50% weaker than those observed; however, the inertial oscillation amplitudes are closely matched. Noteworthy is the slight delay in the modeled inertial response following the cyclone s passage, Figure 14. Observed (gray) and modeled (black) crossshore baroclinic currents at moorings M2 (top) and M4 (bottom).

14 27-14 DAVIDSON AND HOLLOWAY: INFLUENCE OF TROPICAL CYCLONES ON INTERNAL TIDES Figure 15. Observed (gray) and modeled (black) alongshore total currents (total) at moorings M2 (top) and M4 (bottom). which could be attributed to uncertainty in the model wind fields. The baroclinic tidal oscillations do not show a clear spring-neap signal as in the barotropic case in both model and observations. In general the model underestimates the amplitude of the internal tide. In the along-shore direction (Figure 15) the model reproduces the changes in alongshore velocity associated with the cyclone s passage and the ensuing inertial oscillations. The model overestimates the response to the cyclone at M4 in shallow water but not at M2. Again, this overestimation is most likely to be due to errors in the wind field model. 4. Conclusion [52] In the summer of 1995 two mooring arrays recorded the water column response to severe Tropical Cyclone Bobby s passage over the Western Australian Shelf, a region of strong internal tides. We have presented the observations from these moorings in conjunction with modeling the coastal ocean s response to Tropical Cyclone Bobby with an emphasis on the internal tide and near inertial response. [53] The Tropical Cyclone produces a strong inertial response to the water column at the mooring sites one of which was on the cyclones path in 300 m water depth (Figure 1). As observed by others for the open ocean, the cyclone first produces a slight dip of middepth isotherms by m followed by a rapid rising of up to 100 m in 5 hours. As the cyclone moves away, the elevated isotherms subside gradually as inertial oscillations are generated. Model-data comparisons show good agreement for the initial response to Tropical Cyclone Bobby. The inertial response at the shallower mooring site (125 m) is more rapid than that at the deeper mooring site (300 m), which was directly in the path of the cyclone. [54] Changing stratification induced by a tropical cyclone modifies the generation and propagation of the internal tide. Over the shelf the cyclone can cause strong vertical mixing from the combination of wind forcing and the shallow water depth. A density front develops at the shelf break separating well-mixed shelf water and stratified continental slope water. Stratification on the outer shelf can strengthen, despite strong vertical mixing during the cyclone, provided the cyclone draws cold continental slope water on to the shelf. This happens for a cyclone traveling over the shelf producing surface divergence on the shelf, thereby drawing deeper slope water onto the shelf. The presence of the slope affects the response to the cyclone by requiring water to be advected up or down the slope. Following the cyclone passage at the mooring locations, inertial motions dominate over tidal motion as evidenced in isotherm displacement (Figure 5). [55] Both model and data show diminished baroclinic M 2 cross-shore velocity amplitude following the cyclone at the observed mooring locations due to Tropical Cyclone Bobby. However, as indicated in our idealized cyclone studies, the passage of the tropical cyclone can enhance or diminish the internal tide depending on the generation location of the internal tide with respect to the cyclone track. Offshore shore-parallel cyclone tracks and cross-shore cyclone tracks appear to enhance the internal tide. Cyclones tracking over the shelf however appear to reduce the generation of internal tides. [56] We surmise that the mechanism by which a cyclone modifies the generation of the internal tide is by modifying the stratification and hence modifying the slope of internal wave characteristics with respect to bottom slope (Figure 11). In some locations where the slope of characteristics become critical following the cyclone, the internal tide will be enhanced. In other locations, where the cyclone modifies the slopes of characteristics to values away from critical, the internal tide will be reduced. Modal analysis at the mooring sites reveal a decrease in baroclinic wave speeds by up to 6% for the first mode and up to 20% for the second mode, indicating that in the wake of the cyclone, propagation of internal tides has also changed. [57] Over the shelf, cyclones generally mix the water column, eliminating stratification and blocking the propagation of the internal tide onto the shelf, since characteristic slopes would be near vertical in mixed water. The strong density front that exists at the top of the shelf break could lead to reflection of shoreward propagating internal waves away from the shelf. [58] While momentum from the cyclone is not sufficient to enhance mixing down to 1000 m, the cyclone can still affect stratification in deeper water by upwelling and downwelling owing to surface divergence and convergence. This phenomenon can modify shelf slope stratification,