tidal characteristics in bass strait, south-east australia

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Estuarine, Coastal and Shelf Science 114 (2012) 156e165

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Estuarine, Coastal and Shelf Science

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Tidal characteristics in Bass Strait, south-east Australia

E.M.S. Wijeratne a,*, C.B. Pattiaratchi a, Matt Eliot a, Ivan D. Haigh a,b

a School of Environmental Systems Engineering and UWA Oceans Institute, The University of Western Australia, 35 Stirling Highway, M470, Crawley 6009, AustraliabOcean and Earth Science, National Oceanography Centre, University of Southampton, Southampton, UK

a r t i c l e i n f o

Article history:Received 8 January 2012Accepted 31 August 2012Available online 13 September 2012

Keywords:direct gravitational tidal forcinghalf-wavelength resonancetideesurge interactionbarotropic hydrodynamic modelBass StraitAustralia

* Corresponding author.E-mail address: [email protected] (E.M.S.

0272-7714/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.ecss.2012.08.027

a b s t r a c t

We used a two-dimensional, barotropic, numerical model to examine the complex behaviour of the tidesin Bass Strait. Bass Strait, located in south-east Australia between the Australian continent and Tasmania,has the appropriate dimensions to create a half-wave tidal resonance for the M2 tides. The M2 tidal wave(amplitude < 0.4 m) enters the strait from both strait openings, increasing the M2 tidal amplitudetowards the central northern Tasmanian coast to a maximum of w1.1 m. The tidal phases and currentellipses in the strait showed theM2 tides resembled a half-wavelength resonance in a curved, open basin.The semidiurnal, S2, and diurnal, K1 and O1, tidal amplitudes were comparatively small (<0.2 m),progressive in nature and mostly constant through the strait. The model simulations revealed that whenonly open boundary tidal (OBT) forcing was included in the model, the model over predicted the M2

amplitudes by w10e15% in the strait’s central region; when OBT and direct gravitational tidal (DGT)forcing were included, the model accurately reproduced the observed tidal amplitudes. DGT forcing wasused to generate resonantly amplified M2 tides (amplitudes of 0.1e0.3 m) locally, with destructiveinterference between the OBT-forced and DGT-forced tides occurring in the centre of the strait. Themodel simulations also revealed that storm systems propagating west to east attenuated the M2 tidalamplitudes in the strait. The greatest decrease in the tidal amplitudes occurred along the centralnorthern Tasmanian coast and was attributed to tide surge interaction and resonance behaviour in thestrait.

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1. Introduction

1.1. Bass Strait

Bass Strait is a shallow (mean depth w60 m) sea in south-eastAustralia, which separates Tasmania from the mainland (Fig. 1).The mean width (distance between the mainland and Tasmania) isw250 km, and the median line arc length (distance between the200 m depth contours on the strait’s eastern and western sides) isw550 km. The tides in Bass Strait are mainly semidiurnal, witha form factor, F< 0.25 (Pugh,1987). TheM2 tidal constituent, whichdominates the tides, has an amplitude ofw0.2e0.4 m at the strait’sends, increasing to a maximum of w1.1 m along the centralnorthern Tasmanian coast (Fandry et al., 1985; AustralianHydrographic Service, 2011). The semidiurnal, S2, and diurnal, K1and O1, tidal amplitudes are small (<0.2 m) and mostly constantthrough the strait. Strong tidal currents (>2.5 ms�1) have beenrecorded at the strait’s south-east and south-west openings (http://www.tidetech.org/bass-strait-tidal-streams), whereas weak tidal

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currents and long flushing times (w160 days) have been recordedin the central region (Sandery and Kämpf, 2005).

Several observational and numerical studies on tides and theirrelated dynamics in Bass Strait have been undertaken (e.g. Jones,1980; Fandry, 1982; McIntosh and Bennett, 1984; Fandry et al.,1985). All these modelling studies found close agreement for thediurnal component of the tides when they were compared withmeasured values; however, the M2 semidiurnal component wasoverestimated by w10e20%. McIntosh and Bennett (1984) andFandry et al. (1985) attributed this discrepancy in the M2 semi-diurnal tides to uncertainty in the bathymetry, friction parame-terization, and open boundary forcing. They also suggested theerror resulting from the use of approximate dynamical equationswas larger than the error introduced by inadequate open boundarydata and bathymetry. Fandry et al. (1985) proposed the superpo-sition of two opposingM2 Kelvin waves led to resonantly amplifiedtidal amplitudes in the centre of the strait; however, the transversevariation of tidal amplitudes in the strait and the presence of higherM2 amplitudes along the central northern Tasmanian coast have notbeen adequately explained to date.

During severe storms, large (0.5e1.0 m), semidiurnal signalshave been detected in the de-tided sea level residual band in the

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Fig. 1. Map of the study area showing the bathymetry (in metres) and tide gauge sites(C). The inset shows the domain of the hydrodynamic model.

E.M.S. Wijeratne et al. / Estuarine, Coastal and Shelf Science 114 (2012) 156e165 157

centre of Bass Strait. McInnes and Hubbert (2003) suggested thatenhanced westerly currents during strong cold fronts interactedwith the tidal currents to displace the tidal node eastward fromBass Strait, resulting in a tidal phase displacement; however,a quantitative analysis of the effects of this displacement on thetidal dynamics has not been undertaken.

We used a two-dimensional, barotropic, hydrodynamic modelto examine how different forcing components interacted in thestrait and how direct gravitational tides affected the total tides inthe strait. We also examined the effects of the strait’s curvature onthe half-wave tidal resonance and the effects of the tideesurgeinteraction on the tidal dynamics in the strait to determine why:(1) previous tidal models overestimated the M2 tidal amplitudes inthe centre of the strait; (2) M2 amplitudes were higher along thecentral northern Tasmanian coast; and (3) large, semidiurnalsignals were present in the de-tided sea level residual band duringstorms.

The numerical model set-up is outlined in Section 2, and themodel results are presented in Section 3. We discuss the modelresults and address the study objectives in Section 4, and presentour conclusions in Section 5.

1.2. Direct gravitational and open boundary-forced tides

Direct gravitational forced tides are the result of the gravita-tional forces of the Moon and Sun on the water in a particular shelfsea itself, whereas co-oscillating tides represent tides, whichpropagate in and out into the basin from the adjacent oceanthrough the open boundaries.

If the basin is completely enclosed, only DGT forcing cangenerate tides, for example, in Loch Ness, Scotland (Pugh et al.,2011); these DGT-forced tides are called independent tides(Garrett, 1975), a process also known as local tidal potential (e.g.Gouillon et al., 2010).

In most numerical studies of tides in coastal regions, OBT forcinghas been used to force the tides, and DGT-forced tides generated inbasins have often been overlooked. Incorporating DGT forcing into

model equations of motion allows the capture of the free tidalresponse and tides generated specifically in a basin. This approachimproves simulations when modelling large spatial scales or shelf-boundary transitions (Garrett, 1975; Gouillon et al., 2010).

Slater (1985) showed the contribution of OBT forcing to the totaltide was minor compared with the contribution of the DGT forcingin the Cretaceous Seaway of North America. Candela (1991) showedthe integrated contribution of the co-oscillating tide forced atGibraltar Strait wasw10% of the directly generated tidal amplitude.In contrast, a resonantly amplified DGT component can greatlyaffect the local tides, especially in shelf seas that have naturalperiodicity close to the forcing tidal frequencies, for example, thecontinental shelf between Itajai and Santos, Brazil (Huthnance,1980); the Celtic Sea and Bristol Channel (Heath, 1981); the Gulfof Tartary, Sea of Japan (Odamaki, 1989); the EasternMediterranean(Tsimplis et al., 1995); and the Gulf of Mexico (Gouillon et al., 2010).

Depending on the relative phases and magnitudes of the OBTand DGT forcing, the interaction of different forcing componentsmay lead to tides amplifying or attenuating in bays and shelf seas(Odamaki, 1989; Cummins et al., 2010; Gouillon et al., 2010); thustides in a tidal resonant system similar to Bass Strait could bepredicted more accurately if DGT forcing were included in themodel equations.

1.3. Tidal resonance

Resonant effect is the main mechanism for anomalously strongtides in many bays and shelf sea straits, for example, Ungava Bay,Canada (Arbic et al., 2007); the Bay of Fundy (Garrett, 1972); SharkBay, Western Australia (Burling et al., 2003), and the Taiwan Strait(Lin et al., 2001). Resonance tide occurs if the tidal period is close toone of the eigenmodes of the basin.

In bays or shelf seas open at one end, the superposition ofincident and reflected waves produces standing waves throughquarter-wave resonance phenomena, in which the nodal point (orsection) occurs at the mouth (or shelf edge) and the anti-nodeoccurs at the head (or on the coast). The quarter-wave resonancephenomenon generates large tides in the Bay of Fundy, whoselength is nearly equal to one-quarter of the semidiurnal tides’wavelength (Garrett, 1972). In shallow coastal bays, tidal propaga-tion has often been viewed as the superposition of incident andreflected waves under the influence of friction, for example, SanFrancisco Bay (Walters et al., 1985) and Puttalam Lagoon, Sri Lanka(Wijeratne and Rydberg, 2007).

Two oppositely travelling tidal waves entering both ends ofa strait produce half-wavelength resonant tides in the strait, forexample, Hudson Strait (Arbic et al., 2007; Cummins et al., 2010),Taiwan Strait (Lin et al., 2001), and Bass Strait (Fandry et al., 1985).In half-wave resonant, the nodal section occurs at the strait’s endsand the anti-node section occurs in the centre of the strait.

Johns and Hamzah (1968) studied the characteristics of standingwaves in a curved canal and found the canal’s curvature induceda spectrum of transverse oscillations, which enhanced the localwave amplitude at the outer side of the curvature. They alsoshowed the oscillation period of a curved canal resembled that ofa rectilinear canal, which consisted of a length equal to that of themedian line along the curved canal; thus the transverse variation oftidal amplitudes or the occurrence of large amplitudes along thecentral outer shoreline in curved basins such as Bass Strait cannotbe attributed purely to the Kelvin wave effect.

1.4. Tideesurge interaction

Studies have suggested that nonlinear interaction between tidesand surges affects the heights and shapes of storm surges along the

Table 1The model set-up, which included direct gravitational tidal (DGT) forcing, openboundary tidal (OBT) forcing, and atmospheric forcing (AF).

Simulation DGT OBT AF Model domain/bathymetry Model period

1 Yes Yes Yes Covering all Australia/actual 1970e20092 No Yes Yes Covering all Australia/actual 2003e20043 Yes No No Covering all Australia/actual 2003e20044 Yes Yes No Covering all Australia/actual 2003e20045 No No Yes Covering all Australia/actual 20036 No Yes* No Bass Strait/simplified, curved,

open canalMayeJune 2003

* Synthetic M2 tidal wave forcing.

E.M.S. Wijeratne et al. / Estuarine, Coastal and Shelf Science 114 (2012) 156e165158

coast (Johns et al., 1985; Pugh, 1987; Bernier and Thompson, 2007;Horsburgh andWilson, 2007; Jones and Davies, 2008). Here the seasurface elevation either increases above or decreases below itsoriginal storm surge value and changes the tidal amplitude. Howmuch the tidal amplitude changes depends on the storm strength,wind direction, bathymetry, and local tidal conditions (Bernier andThompson, 2007; Horsburgh and Wilson, 2007; Jones and Davies,2008). Ruessink et al. (2006) showed that wind-driven flowenhanced friction during the flood phase of a tidal cycle morethan it reduced friction during the ebb flow, thereby increasingthe friction over the tidal cycle and reducing the tide current range.Jones and Davies (2008) showed that changes in the bottomstress affected tidal elevations and currents in shallow seas duringstorms.

Generally, only non-tidal signals (surges, seiches, and otherweather components) are present in the de-tided sea level residualband; however, damped or amplified tides resulting from tideesurge interaction during storms could remain in the sea levelresidual band as a semidiurnal signal (e.g. Wang and Chai, 1989).Zhang et al. (2010) showed that tideesurge interaction in theTaiwan Strait caused semidiurnal oscillations in the sea levelresidual band. McInnes and Hubbert (2003) examined tide gaugedata and showed that semidiurnal oscillations remained in the sealevel residuals during storms in Bass Strait, with larger oscillationsrecorded along the central northern Tasmanian coast.

2. Numerical model

2.1. Model set-up

A depth-averaged tideesurge model for the whole Australiancoast (see Fig. 1) has been developed using the Danish HydraulicInstitute’s MIKE21 FM (flexible mesh) suite of modelling tools. TheMIKE21 FM model is based on the numerical solution of theincompressible Reynolds-averaged, NaviereStokes equationsinvoking the assumptions of Boussinesq and hydrostatic pressure(see Danish Hydraulic Institute, 2010, for more details).

The bathymetric data used for the model were obtained fromGeoscience Australia’s nine-arc second (250 m) dataset (Websterand Petkovic, 2005). The grid resolution was chosen based on theregion’s coastal topography and local water depth variability andhad a resolution of w20e30 km at the open ocean boundaries,decreasing to <2.5 km along the whole Australian coast. In BassStrait, the grid resolution varied between 2.5 and 4 km.

Astronomical tidal levels derived from the TPX07.2 global tidalmodel were used to force themodel at the open boundaries (Egbertet al., 1994; Egbert and Erofeeva, 2002). This forcing included eightprimary tidal constituents (M2, S2, N2, K2, K1, O1, P1, and Q1), twolong-period constituents (Mf and Mm), three shallow-waterconstituents (M4, MS4, and MN4), and an additional 16 minortidal constituents (2Q1, s1, r1, M1, c1, p1, f1, q1, J1, OO1, 2N2, m2, n2, l2,L2, and s2), which were inferred from the eight tidal constituents.The model formulation also included the direct effect of the tide-generating astronomical forcing, which was prescribed througha tide-generating potential term in the modelling tools.

The model-forced, atmospheric forcing (AF) data (pressure andwind components) were obtained from the US National Center forEnvironmental Prediction (NCEP) global reanalysis (Kalnay et al.,1996). These meteorological fields were available every 6 h andhad a horizontal resolution of 2.5�. We used Manning’s roughnesscoefficient (0.32 m1/3s�1) to specify the model’s bed resistance. Themodel minimum time step was set to 0.1 s and the maximum to900 s. The model was set to output the sea level and currents (east-west and north-south components) for all grid points at one-hourintervals.

As part of our study on estimating the current extreme sea levelexceedance probabilities around the coastline of Australia (Haighet al., 2012), the model was run for a continuous period of 40years (from 1970 to 2009) and included all forcing agents (AF, DGTforcing, and OBT forcing). The model was validated using obser-vations from 29 tide gauge sites around Australia with long (>30years) records (Haigh et al., 2012). Several other simulations wereundertaken (see Section 2.2 and Table 1) to determine the internalresponse of the Bass Strait tides to AF, DGT forcing, and the strait’scurved topography. A comparison of the measured and predictedtides around Bass Strait is presented in Section 3.1.

2.2. Experimental set-up

Six model runs (see Table 1) were undertaken including andexcluding the three main forcing terms: AF, DGT forcing, and OBTforcing. Simulation 1, the most realistic model configuration,included AF, DGT forcing, and OBT forcing. Simulation 2 included AFand OBT forcing, but excluded DGT forcing; most modelling studiesof shallow seas have used this configuration, and it also corre-sponded with past Bass Strait modelling studies (e.g. Fandry et al.,1985). In simulation 3, only DGT forcing was included. Simulation4 combined DGT and OBT forcing, but excluded AF, and in simula-tion 5, only AF was included.

An idealised model simulation (simulation 6) was also per-formed to examine resonance behaviour in a curved, open basinrepresentative of Bass Strait. The model dimensions were chosen toresemble the local geometry of Bass Strait. AF, DGT forcing, theCoriolis effect, and the transverse variation of the tides at the openboundaries were all excluded for this simulation. The idealisedmodel was forced at the open boundaries with a synthetic M2 tidethat had an amplitude of 0.4 m and a phase of 40�.

2.3. Data analysis methods

The predicted sea level and current time series at every modelgrid point were subjected to harmonic analysis using the T-TideMATLAB toolbox (Pawlowicz et al., 2002). To visualise and interpretthe model results for Bass Strait, co-tidal charts for the main tidalconstituents,M2, S2, K1, and O1, were produced and the tidal currentdata were transformed into tidal ellipse parameters for the phase(q), orientation (q), semi-major axis (A), and semi-minor axis (B).

To calculate the sea level residuals: (1) we subtracted the tidalcomponent (harmonically predicted) from the tide gauge obser-vations or predicted sea level and (2) subtracted the model runsthat included only tidal forcing (simulation 4) from the model runsthat included tidal and atmospheric forcing (simulation 1). The sealevel residuals consisted of surges, seiches, and other noise andweather components. We filtered the sea level residual further toremove the lower frequency fluctuations (>32 h) and to isolate thesemidiurnal oscillations that occurred during storms.

Table 2The harmonic tidal constituents calculated from the tide gauge data and predicted(from simulations 1 and 2) sea level data at the Bass Strait sites. The amplitudes (inmetres) and phase lags (in italics) are in degrees with respect to the Greenwichtransit of the moon.

Site M2 S2 K1 O1

Burnie Tide gauge 1.1440�

0.14187�

0.16302�

0.12277�

Simulation 1 (DGT þ OBT þ AF) 1.1442�

0.14194�

0.17296�

0.13282�

Simulation 2 (OBT þ AF) 1.2832�

0.18210�

0.17286�

0.14265�

George Town Tide gauge 1.0949�

0.13204�

0.16311�

0.12280�


0.13203�

0.17299�

0.14283�


0.14220�

0.17314�

0.14265�

Lonsdale Tide gauge 0.4436�

0.13158�

0.14279�

0.10261�


0.12166�

0.14272�

0.12265�


0.12143�

0.14265�

0.11284�

Hobart Tide gauge 0.24309�

0.01244�

0.21291�

0.14270�


0.01249�

0.25282�

0.22281�


0.01252�

0.25278�

0.22278�


3. Results

3.1. Tide gauge and predicted data comparison

Table 2 shows the measured and predicted tidal constituentsfrom simulations 1 and 2 for the six tide gauge sites around BassStrait. Here themeasured and predicted continuous data from 2003to 2004 were used to perform a harmonic analysis. As expected, thepredicted tidal phases and amplitudes from simulation 1 (whichincluded AF, DGT forcing, and OBT forcing; see Table 1) corre-sponded with the measured data for all the major tidalconstituents.

The results from simulation 2 (which included AF and OBTforcing, but excluded DGT forcing) showed the M2 tidal amplitudesin the centre of the strait were w10e15% higher than they were insimulation 1 and the tide gauge data. For example, at George Town(Fig. 1), simulation 2 predicted M2 amplitude of 1.25 m; simulation

Fig. 2. The measured and predicted sea level residuals for 2003 at (a) Victor Harbor; (b) Londata; the red lines denote the results from simulation 1; and the blue lines denote the res

1 predicted M2 amplitude of 1.08 m; and the tide gauges recordedM2 amplitude of 1.09 m. The S2 amplitude from simulation 2 wasalso slightly higher than it was in simulation 1 and the tide gaugedata; however, the K1 and O1 tidal amplitudes resembled the tidalamplitudes from the tide gauge data. The results from simulation 2corresponded with the results from McIntosh and Bennett’s (1984)and Fandry et al.’s (1985) modelling studies. These results showedthat when DGT forcing was included in the model, the modelaccurately reproduced the observed tides in Bass Strait.

The measured and predicted (from simulations 1 and 2) sealevel residuals for Victor Harbor, Lonsdale, Burnie, and Hobart for2003 are shown in Fig. 2. The model’s performance was evaluatedusing model skill levels (Willmott, 1984). The skill levels >0.90(Fig. 2) showed that both model configurations (simulations 1 and2) captured the main characteristics of the storm surges thatoccurred through the year; however, both simulations slightlyunderestimated the peak of the highest storm surge events. Thisunderestimate may have been due to the coarse temporal (six-hourly-averaged) and spatial (2.5�) scale of the NCEP atmosphericforcing. A comparison between the measured and predictedfrequency oscillations in the sea level residual band is presented inSection 3.3.

3.2. Tidal propagation and resonance

Fig. 3 shows the predicted co-tidal charts for the M2 and K1tides for simulations 1 to 3. The charts for simulations 1 (Fig. 3aand b) and 2 (Fig. 3c and d) revealed the M2 tidal wave propa-gated south along Australia’s east coast as a Kelvin wave. Part ofthis wave was refracted westward at the strait’s eastern end whilethe main part of the wave moved clockwise around the Tasma-nian coast and was then refracted eastward at the strait’s westernend. The M2 amplitude at the strait’s eastern end was w0.4 m,and the M2 amplitude at the strait’s western end was w0.2 m. TheM2 tidal amplitudes increased from the strait’s eastern andwestern ends towards the centre of the strait and also towardsthe southern shoreline (i.e. the northern Tasmanian coast). Thehighest amplitudes occurred along the central northern Tasma-nian coast.

The K1 tide propagated as a Kelvin wave from west to eastthrough the strait, with slightly higher amplitudes occurring alongthe Victorian coast (Fig. 3b and d). The K1 tidal wave was refractedat the strait’s western end and travelled anticlockwise around

sdale; (c) Burnie; and (d) Hobart. The black lines denote the results from the tide gaugeults from simulation 2.

Fig. 3. Tidal amplitudes (in metres black lines) and phases (in degrees red lines) around Bass Strait calculated from the model simulations. (a) & (b) the M2 and K1 tidal componentsfrom simulation 1 (which included atmospheric forcing, direct gravitational tidal forcing, and open boundary tidal forcing); (c) & (d) the M2 and K1 tidal components fromsimulation 2 (which included atmospheric forcing and open boundary tidal forcing); (e) & (f) theM2 and K1 tidal components from simulation 3 (which included direct gravitationaltidal forcing only). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


Tasmania towards Australia’s east coast. The S2 and O1 (not shown)tidal constituents also had similar wave propagation characteristicsto the K1 tides. The K1 tidal amplitudes predicted in simulations 1(Fig. 3b) and 2 (Fig. 3d) were similar, which revealed that DGT hasno effect on K1 amplitudes. The M2 tidal amplitudes recorded insimulation 1 (Fig. 3a) differed from those recorded in simulation 2(Fig. 3c); simulation 2, which excluded DGT forcing, over predictedthe tidal amplitudes in the strait, especially along the centralnorthern Tasmanian coast (Burnie and George Town; see Table 2).Fig. 3e and f show the M2 and K1 tidal phases and amplitudescalculated from simulation 3, which included DGT forcing only. TheM2 tide (Fig. 3e) had amplitudes between 0.1 and 0.3 m (witha maximum recorded off the central northern Tasmanian coast),and the S2 tide (not shown) had a maximum amplitude of w0.1 m;however, no diurnal tides were generated.

To assess the tides’ resonance behaviour in Bass Strait, weexamined the tidal current ellipse characteristics from two modelconfigurations: (1) the Bass Strait model, which included realtopography and DGT and OBT forcing (simulation 4; Table 1); and(2) an idealised model, which was representative of Bass Strait, butincluded a curved channel (simulation 6; Table 1). Fig. 4 shows theM2 and K1 tidal current ellipses’ semi-major axis speeds obtainedfrom simulation 4. The ellipses (shown in black) were included atselected points across the domain to show the tidal current’sgeneral circulation pattern. Our results from Fig. 4a showed: (1) theM2 tidal currents were strongest at the strait’s south-east andsouth-west ends; (2) the east-west direction M2 current compo-nents were aligned in opposite directions at the strait’s eastern andwestern and ends; and (3) the M2 current ellipses were weakenedtowards the centre of the strait and oriented to the strait’s

Fig. 4. The semi-major axis speeds for the (a) M2 and (b) K1 current ellipses aroundBass Strait calculated from simulation 4. The colours denote the semi-major axisspeeds, and the ellipses (in black) are plotted at selected cells. The lines extending fromthe centre of the ellipses represent the current’s direction and speed at the time oflocal high sea level.

Fig. 5. The M2 tidal amplitude and current ellipses from the idealised model.


transverse axis. The phases and orientations of the tidal currentellipses showed the M2 tides at the strait’s open ends wereprogressive in nature and the M2 tides in the centre of the straitwere standing in nature.

The K1 currents (semi-major and semi-minor axes) were weakthroughout the strait (Fig. 4b), and the current ellipses developedgradually in one direction (west) through the strait. The K1 currentswere stronger near the Victorian coast than they were to the southof the strait. The S2 and O1 tidal current ellipses (not shown) alsohad similar characteristics to the K1 tide.

Fig. 5 shows theM2 tidal amplitude and current ellipses from theidealised model experiment (simulation 6; Table 1). The tidalamplitude increased towards the centre of the strait and wasstrongest along the central outer shoreline (i.e. off the centralnorthern Tasmanian coast). The tidal amplitude along the outershoreline was 20% higher than it was along the inner shoreline (i.e.the Victorian coast). The currents ellipses were rectilinear, and thecurrents’ eastewest components were aligned in opposite direc-tions at the strait’s eastern and western ends. The currents werestronger in the strait’s south-west and south-east corners. Thecurrents in the centre of the strait were oriented towards the outershoreline. These results suggested the idealised model withsimplified topography (without the Coriolis effect) could simulatethe main resonance behaviour features of M2 tides in Bass Strait.

Fig. 6. The tide gauge and modelling results (from simulations 1, 2, and 5) showing thetide levels and sea level residuals between 28 May and 10 June 2003. (a) The measuredand predicted tides (based on tidal constants) for Victor Harbor; (b) the sea levelresiduals from the tide gauge and predicted data for Victor Harbor; (c) the measuredand predicted tides (based on tidal constants) for Lonsdale; (d) the sea level residualsfrom the tide gauge and predicted data for Lonsdale; (e) the measured and predictedtides (based on tidal constants) for Burnie; (f) the sea level residuals from the tidegauge and predicted data for Burnie.

3.3. Sea level residuals during storms

The storm surge series (Fig. 2) showed sea level oscillationsoccurred during surge events at the Burnie and Lonsdale tidestations. Herewe examine the oscillations produced during a storm

that occurred between 5 and 8 June 2003. Fig. 6 shows the timeseries of the measured and predicted tides (using tidal harmonics)and the measured and predicted (from simulations 1, 2, and 5) sealevel residuals for Victor Harbor, Lonsdale, and Burnie from 28 Mayto 10 June 2003. During the storm, the semidiurnal sea level ranges


were significantly damped at Burnie (Fig. 6e) and slightly dampedat Lonsdale (Fig. 6c); however, no damping was observed at VictorHarbor (Fig. 6a), which is located outside the strait.

The measured and predicted sea level residuals for VictorHarbor, Lonsdale, and Burnie are shown in Fig. 6b, d, and f,respectively. The sea level residual obtained from the tide gaugedata showed the highest surge occurred at Victor Harbor (Fig. 6b).The surge levels at Lonsdale and Burnie were low; however, largesemidiurnal oscillations were observed in the sea level residualband. This result revealed that tidal damping during the stormcaused the semidiurnal oscillations in the sea level residual band.The sea level residuals at Lonsdale (Fig. 6d) and Burnie (Fig. 6f),derived from model simulations 1 and 2 (Table 1), reproduced thesemidiurnal signal in the sea level residual band during the storm;however, simulation 5 (which included only AF) did not reproducethis feature.

Fig. 7 shows the distribution of the sea level residual at differenttimes during the storm and the sea level residual range on 7 June2003. The sea level residual levels were high at 0000 h (Fig. 7a), lowat 0600 h (Fig. 7b), and high again at 1200 h (Fig. 7c). The semi-diurnal sea level residual range (difference between the lowest andhighest sea level residuals) on 7 June 2003 (Fig. 7d) showed thesemidiurnal sea level residual component (i.e. the damped tidalrange) increased towards the centre of the strait, with the highestrange (>0.6 m) occurring along the central northern Tasmaniancoast.

3.4. M2 tidal attenuation

Fig. 8a shows the M2 tidal amplitudes along the Victorian andnorthern Tasmanian coasts, which were extracted from the modelsimulations (using 2003e2004 continuous data) that included AF(simulation 1) and excluded AF (simulation 4). The results showed

Fig. 7. The sea level residuals for Bass Strait on 7 June 2003 at (a) 0000; (b) 0600; and (c) 120

that atmospheric forcing attenuated the M2 tide by 0.02e0.04 m tothe north and south of the strait (stations V28eV55 along Victoria’ssouth coast and stations T33eT53 along the northern Tasmaniacoast); however, no tidal attenuation occurred at the stationslocated outside the strait. The largest decrease in tidal amplitude(w0.04 m) occurred along the central northern Tasmanian coast(Fig. 8b). Here, we used classical harmonic analysis method (seePugh,1987) to estimate the tidal constituents from time series (tidegauge and predicted sea levels), hence estimated tidal amplitudesrepresented the mean value for whole period (i.e. over periods ofboth calm and storm conditions); however the analysis could beimproved using a method that can capture the time variability ofthe harmonic coefficients, such as wavelet analysis (e.g. Foremanet al., 2009).

4. Discussion

4.1. Impact of DGT forcing on M2 tides

The results from simulations 1 and 2 revealed that when onlyOBT forcing was included in the model, the model over predictedthe M2 amplitudes by w10e15% in the centre of the strait; theseresults corresponded with the results fromMcIntosh and Bennett’s(1984) and Fandry et al.’s (1985) studies. When DGT forcing wasincluded in the model, the model accurately reproduced theobserved tidal amplitudes. The results from simulation 3 revealedthat DGT forcing generated strong, resonantly amplifiedM2 tides inBass Strait.

Odamaki (1989) showed a phase difference of 180� causeddestructive interference between OBT and DGT components,resulting in low M2 amplitudes in the Gulf of Tartary, Japan.Gouillon et al. (2010) also showed constructive and destructiveinterference between DGT and OBT forcing amplified and

0. The semidiurnal sea level residual range for Bass Strait on 7 June 2003 is shown in (d).

Fig. 8. (a) The M2 tidal amplitudes along the Victorian coast (stations V1eV66) andnorthern Tasmanian coast (stations T33eT53) from the simulations including only tidalforcing (red line) and both tidal and atmospheric forcing (black line); (b) the distri-bution of the M2 amplitude difference from the simulations with and without atmo-spheric forcing. (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)


attenuatedM2 tides in the Gulf of Mexico. The superposition of twowaves of the same frequency can be expressed as:

hðtÞ ¼ hiðtÞ þ hoðtÞ ¼ aisin ðut� qiÞ þ aosin ðut� qoÞ

where h is the combined sea level at time, t; hi is the sea level forcedby direct gravitational tides; ho is the sea level forced by openboundary tides; u is the selected tidal constituent’s frequency; a isthe selected tidal constituent’s amplitude; and q is the selected tidalconstituent’s phase.

For the M2 tidal constituent in the centre of Bass Strait, the DGTamplitude (ai) was w0.3 m; the OBT amplitude (ao) was w1.2 m;the DGT phase (qi) was w180�; and the OBT phase (qo) was w40�.The phase difference wasw140�; thus we expected the destructiveinterference between the two forcing components to cause atten-uation. The resultant amplitude (a) was w1.1 m. For the M2 tidalconstituent at the strait’s western end, constructive interferencefrom the OBT and DGT components occurred because the phasedifference was <90�. At the strait’s eastern end, the phase differ-ence was w180�; hence destructive interference occurred. BassStrait consists of direct gravitational-forced tides and openboundary-forced tides; thus we believe DGT and OBT forcing

should be included when using hydrodynamic models to predictthe tides and related dynamics in Bass Strait.

4.2. Impact of strait curvature on tidal resonance

The tidal phases and current ellipses in Bass Strait suggested theM2 tide was a progressive wave at the strait’s western and easternends and a standing wave in the centre of the strait. Bass Strait isa curved, open canal, with the Victorian coast forming the innerboundary and the northern Tasmanian coast forming the outerboundary (Fig. 1). The wavelength (l) of a tidal wave is given asl ¼ 2pgh/s, where g is acceleration due to gravity; h is the meanwater depth; and s is the tidal component’s angular frequency(radians s�1). The mean water depth is w60 m; thus the wave-length (l) is w1100 km for the M2 tidal constituent(s ¼ 1.405 � 10�4 s�1). The Bass Strait median line arc length (thedistance between the 200 m contour through the eastern andwestern sections of Bass Strait) is w550 km; thus the strait has theappropriate geometric dimensions for half-wavelength resonancein the semidiurnal period.

Johns and Hamzah (1968) showed the oscillation period ofa curved canal resembled that of a rectilinear canal, which hada length equal to that of themedian line along the curved canal. Thehalf-wavelength resonance period (T) for an open-end canal isgiven as T ¼ ð1=nÞ2L= ffiffiffiffiffiffi

ghp (Pugh,1987), where L is the canal length

and n is the mode number, with n ¼ 1 for the fundamental mode;hence the fundamental mode of the half-wavelength resonanceperiod in the strait is w12.5 h.

Another approach to determine the dominant resonantfrequency of a system is to examine its response to a range offorcing frequencies (Garrett, 1972; Godin, 1988). Our results forsimulation 3, which included only DGT forcing (Table 1), revealedthe M2 tide was stronger than the other tidal frequencies and thatthe strait’s fundamental period was almost semidiurnal.

The idealised model configuration reproduced the half-wavelength resonance behaviour for curved, open canals (Johnsand Hamzah, 1968). The M2 tidal amplitude along the centralnorthern Tasmanian coast was about four times higher than it wasat the ends of the strait. Anomalously amplified semidiurnal tideshave also been observed near the centre of the western TaiwanStrait (i.e. on China’s east coast) (Lin et al., 2001; Jan et al., 2004).Johns and Hamzah (1968) studied the characteristics of standingwaves in a curved canal and found that curvature in the canalinduced a spectrum of transverse oscillations and enhanced thelocal wave amplitude at the outer side of the curvature.

Fandry et al. (1985) described the transverse variation of M2tidal amplitudes in Bass Strait as Kelvin waves; however, we foundthe strait’s curvature contributed to the transverse variation of theM2 tidal amplitudes. The idealised model simulation (simulation 6)revealed the observed transverse variation of the M2 amplitudecould be reproduced without Coriolis forcing (see also Lin et al.,2001).

4.3. Impact of tideesurge interaction on M2 tide

The tidal damping that occurred during the June 2003 stormshowed the sea level residual had a semidiurnal signal (see alsoMcInnes and Hubbert, 2003). The damping of tidal amplitudesduring storms can be attributed to: (1) decreasing resonanceamplification by the damping of the incident (entering) tidal wave;(2) the amplification of DGT resonance and destructive interferencewith co-oscillating resonance; (3) variation in the tidal currentharmonics when stratification has affected the horizontal current’svertical profile (e.g. Prandle,1982); (4) the decrease of the baroclinic


tidal contribution to the surface tides bydesertification (tidalmixingof the water column); and (5) the generation of semidiurnal seichesby atmospheric forcing (e.g. Luettich et al., 2002).

Baroclinic forcing was unlikely to have caused the large sea levelresidual variations found in the surface tides in Bass Strait becauseof the strait’s shallow depths. Also, during winter, and especiallyduring storms, the strait is vertically well mixed, so density strati-fication would have had little effect on the sea level residuals. Ourresults showed that when AF and OBT forcing were included in themodel, a semidiurnal signal in the sea level residual band duringthe stormwas produced. The simulations that included only AF didnot generate significant semidiurnal sea level oscillations duringthe storm; thus local seiching would not have caused this semi-diurnal signal.

Oscillations of storm surge elevationwith near semidiurnal tidalperiods have also been observed in the Taiwan Strait along thenorth Fujian coast during typhoons (Zhang et al., 2010). Zhang et al.(2010) suggested that strong tidal and storm-induced current alongthe channel direction enhance tideesurge interaction via nonlinearbottom friction. The tideesurge interaction is further intensified bythe channel effect of the Strait, resulting in oscillations along thenorthern Fujian coast.

The tidal currents in Bass Strait were strongest at the strait’seastern and western ends and weaker in the centre of the strait;however, the strongest semidiurnal oscillations in the sea levelresidual band (i.e. the tidal damping) occurred in the centre of thestrait, especially along the central northern Tasmanian coast. Weattributed these large, semidiurnal signals in the sea level residualband to tidal resonance damping during storms. Tideesurge inter-action was strongest at each end of the strait; however, our resultsshowed that a small decrease in the tidal amplitude at theendsof thestrait would greatly decrease the tidal amplitude in the centre of thestrait due to the half-wavelength resonance behaviour in the strait.

5. Conclusions

We performed six barotropic model simulations with differenttidal and atmospheric forcing combinations to study the effect ofthese forcing mechanisms on the tides in Bass Strait. Generally,a numerical model that includes only open boundary forcing couldreproduce the tides in marginal seas where the co-oscillating tidepredominates; however, our results revealed that direct gravita-tional forcing generatedM2 tidal resonance in Bass Strait, where thestrait’s natural periodicity resembles theM2 tidal frequency. TheM2tidal amplitudes in the centre of the strait were accurately repro-duced when the model was forced with open boundary and directgravitational tides; thus we concluded that direct gravitational tidalforcing must be included in numerical models of Bass Strait toreproduce the tidal dynamics accurately.

We also found that half-wavelength resonance in a curved, opencanal amplified the M2 tides in the central northern Tasmaniancoast, and tideesurge interaction at the ends of the strait attenu-ated the M2 tidal amplitudes during storms. Outside the strait,however, tide-surge interaction had less effect on the tides.

Acknowledgements

The model bathymetry was derived from 250-m resolution datafrom Geosciences Australia, and the tide gauge data were obtainedfrom the Australian National Tide Centre. The Australian Depart-ment of Climate Change and Energy Efficiency (through theAntarctic Climate and Ecosystems Cooperative Research Centre)funded this study, whichwas built on an earlier study funded by theWestern Australian Marine Science Institution (WAMSI). We aregrateful to the three anonymous reviewers for their suggestions to

improve this paper. We also thank Ruth Gongora-Mesas for hereditorial suggestions.

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