Propagation characteristics of coastally trapped waves on the Australian Continental Shelf
School of Physical, Environmental, and Mathematical Sciences, University of New South Wales, Canberra, ACT, Australia
Corresponding author: R. H. Woodham, School of Physical, Environmental, and Mathematical Sciences, University of New South Wales, Northcott Drive, Canberra, ACT 2600, Australia. (Robert.Woodham@defence.gov.au)
 Coastally trapped waves (CTWs) are investigated around the Australian coast based on their signature in the sea surface height (SSH) field, using independent data from coastal tide gauge observations and the Bluelink ocean forecasting system from 2009. A high correlation (correlation coefficients from 0.6 to 0.9) between the model and observational data is demonstrated for locations between Hillarys, in the south-west of the continent, and Cape Ferguson, in the north-east. This justifies the use of Bluelink data for the rest of the investigation and enables coastal locations between tide gauge stations to be included. Spectrum analysis shows that CTWs have periods of between 10 and 25 days, with the 10 day period dominating along the south coast, and greater energy around the 20 day period on the east coast. The greatest spectral power is located around the Great Australian Bight. After filtering to isolate these CTW frequencies, phase speeds are estimated using two methods and are consistent with earlier studies. There is a close correlation between the standard deviation of the filtered SSH data and the width of the continental shelf, indicating that CTW amplitudes are strongly modulated by the local shelf width. Contrary to earlier studies, a complex empirical orthogonal function analysis shows that the majority of the variance propagates as continuous features between the south-west and north-east, and although modulated by the shelf width, it is unaffected by the sharply changing coastline orientation, shallow Bass Strait, or wind forcing regions.
 The variability in sea surface height (SSH) along the southern and eastern coasts of the Australian continent, on timescales between one day and several months, is dominated by coastally trapped waves (CTWs) [Hamon, 1962, 1966; Freeland et al., 1986; Maiwa et al., 2010]. These features are initiated by the alongshore wind stress [Adams and Buchwald, 1969], propagate with the coast on their left [Mysak, 1980], and decay through bottom friction [Brink, 1991]. Although CTWs have been reported in other locations around the world [see Wilkin, 1988, and references therein], the east coast of Australia has been a particular area of interest for their study, having been investigated in the 1960s by Hamon [1962, 1966], and later during a dedicated “Australian Coastal Experiment” (ACE), which was the first field experiment specifically designed to detect and characterize CTWs [Freeland et al., 1986]. Maiwa et al.  have continued this interest in Australian CTWs, using observations and numerical model studies to investigate them along the southern and eastern coasts of Australia.
 CTWs are a hybrid form of wave, a cross between internal Kelvin waves and topographic Rossby waves [Brink, 1991]. Topographic Rossby waves, also called barotropic shelf waves [Wilkin, 1988], can form where a sloping seabed provides a relative vorticity gradient, analogous to the latitudinal variation in Coriolis parameter responsible for planetary Rossby waves [Brink, 1991]. Wilkin  has pointed out that the internal Kelvin and topographic Rossby waves define the limits of the range of the CTWs, depending on the stratification, and there are not two distinct types of wave. In a homogeneous ocean (no stratification), barotropic shelf waves are seen, whereas in high stratification, Kelvin waves dominate. In addition to the CTW mode, there is also an external (barotropic) Kelvin wave mode, but they travel much faster than the CTWs.
 Although the basic attributes of CTWs around Australia have been established, some uncertainty remains regarding their detailed propagation characteristics. This is due to several factors, including: the difficulty in finding analytical solutions even to simplified governing equations which describe CTW propagation [Brink, 1991]; the relatively coarse spatial resolution of tide gauge observations, compared to the dimensions of the CTWs; and the complexity of the bathymetry over which the CTWs propagate, which varies on space scales much shorter than the waves themselves. Examples of this last factor include (Figure 1): widely varying continental shelf and slope widths; a section of relatively shallow water, with no continental slope transitioning deeper water, through the Bass Strait; sharp changes in coastal orientation in the south-west and south-east corners of the continent; and the presence of numerous promontories, bays, inlets, and islands. A range of propagation speeds has been reported (in one study, e.g., from 4.5 to 22.6 ms−1 along the south coast [Maiwa et al., 2010]), and there has been some debate in the literature on the mechanism by which the CTWs propagate from the southern to the eastern coasts [Clarke, 1987; Maiwa et al., 2010].
 The basic characteristics of CTWs on the east coast of Australia were determined during the ACE, which was conducted between Gabo Island and Nobby's Head, in the south-east part of the Australian continent (see Figure 1), during the period September 1983 to March 1984. ACE instrumentation included three lines of five current meter moorings, as well as conductivity/temperature/depth (CTD) instruments, eXpendable Bathy Thermographs (XBT), instruments for collecting meteorological observations, coastal tide gauges, and bottom pressure instruments [Freeland et al., 1986]. The ACE found evidence that the low-frequency variability in sea level and currents was dominated by freely propagating CTWs, with typical characteristics reported as: a phase speed of around 2–4 ms−1; a period of around 10 days; a SSH amplitude of around 5–10 cm; and a wavelength of around 2500 km. Freeland et al.  reported northward propagating patterns of longshore current in the ACE data. Contrary to earlier predictions, they also showed that CTW energy was large at the southern end of the ACE array, whilst further north, the CTW energy could be explained largely by propagation of this energy northward as free waves. This shows that CTW energy was entering the ACE domain from the south, whereas the array had been designed on the assumption that CTWs would be generated by wind stress within the array itself. Freeland et al.  considered possible sources of the CTW energy present at Gabo Island, at the extreme south of the ACE array (Figure 1). They argued against the Great Australian Bight, which lies to the west of Bass Strait, as the source region, whence CTWs would then propagate along the continental shelf either around Tasmania or through Bass Strait. Instead, they identified the source mechanism as wind forcing in the Bass Strait itself or over the shelf between the eastern end of Bass Strait and Gabo Island. They also calculated the autocovariance of sea level data at Eden (located 50 km north of Gabo Island), which had been filtered to remove tidal and other high-frequency variation, establishing a dominant period of 5 days.
Clarke  later considered the question of the source of the ACE CTWs in more detail. He found that, although an external Kelvin wave trapped to the north coast of Bass Strait can propagate eastward through the strait, the CTWs are damped by friction in 40 km or less, and therefore cannot. His calculations gave a phase speed of 28 ms−1 and frictional decay scale of 9400 km for the (external) Kelvin wave, and phase speeds of 0.42, 0.097, and 0.048 ms−1 for the first three CTW modes, with frictional decay scales of 40.3, 8.6, and 3.9 km, respectively. Clarke also estimated an upper bound to the proportion of the energy trapped at the southern Australian shelf reaching the western entrance to the Bass Strait, which is subsequently carried to its eastern end, as only 6.8%. He identified the mechanism for this energy transfer through Bass Strait as scattering of CTW energy at the western end into the barotropic Kelvin wave, which he considered to be the only mode capable of transmitting the energy through the strait. He stated that the remaining energy is either frictionally damped in the baroclinic CTW modes, or else it does not enter the strait in the first place. Clarke argues that, since the energy traveling northward along Tasmania's eastern coast is negligible, the CTW energy detected by the ACE array is generated by the winds in the Bass Strait itself, and backs this up with a quantitative analysis.
 A more extensive survey of CTWs for the Australian coast was made by Maiwa et al. , using observations from tide gauges. They noted a seasonal signal from the monsoon in the north of the continent and higher frequency variations in the south. They also report an annual pattern, with CTW amplitudes distinctly larger in winter than in summer. They found that maximum amplitudes of around 70 cm occur between Thevenard and Port Stanvac (Figure 1) and summarize a range of propagation speeds as: 4.5 ms−1 “or faster” on the western and southern coasts, and 2.1–3.6 ms−1 on the east coast. They also identify two main forcing regions: one at the western end of the south coast of Western Australia (in the vicinity of Esperance), and one in the south-eastern corner of the continent (in the vicinity of Bass Strait), with the waves propagating freely both between these two forcing regions, and to the north of the second one, along the eastern coast. They report a “rapid decrease in the wave amplitude as they propagate through the south-eastern corner of Australia,” and also propose that “most of the CTWs in the eastern coast should be considered as waves excited by the wind along the south-eastern region of the continent.”
 Here we propose that CTWs around the southern and eastern part of the Australian continent, between Hillarys in the south-west and Cape Ferguson in the north-east, are, in fact, continuous features, which propagate freely from one end of this expanse of coastline to the other. Only relatively minor changes in phase speed and wavelength are seen, despite the various bathymetric features alluded to above, the changes in coastline orientation, and the imposition of the relatively shallow channel of the Bass Strait. The CTW amplitude reduces somewhat between the southern and eastern coasts, but the majority of this reduction takes place east of Bass Strait, and is not associated either with the strait itself, as postulated by Clarke , or with the change in coastline orientation, as postulated by Maiwa et al. . Furthermore, SSH amplitude is found to be closely correlated with the width of the continental shelf. This indicates that CTWs propagate as continuous features along the coast, but that their amplitude is modulated by the local shelf width. Evidence to support this view is obtained using SSH data from the Bluelink ocean forecasting system [Brassington et al., 2007]. This model data is used to fill in the gaps in SSH observations between adjacent coastal tide gauge stations in the Australian network. Our hypothesis is based on spectrum analysis, and factorization into complex empirical orthogonal functions (CEOFs), after filtering to isolate the CTW frequencies of interest. To support our hypothesis, first, the data and analysis methods are described and the ability of the Bluelink ocean forecasting system to accurately model CTWs is established in section 2, by comparing observed and modeled SSH variability. Next, in section 3, CTW characteristics are established using spectrum analysis and analysis of the filtered data, and evidence is presented that CTWs propagate as continuous features along the southern and eastern coasts of Australia, based on a CEOF analysis. Finally, section 4 summarizes our study and results.
2. Data and Methods
 Observational data from coastal tide gauges and model data from a numerical ocean model provide ground truth and spatial coverage. CTW frequencies are isolated from this data using a Butterworth filter and analyzed by factoring into complex empirical orthogonal functions (CEOFs).
2.1. Bluelink Data
 Sea Surface Height (SSH) data from the Bluelink project [Brassington et al., 2007; Oke et al., 2005, 2008; Schiller et al., 2008] is the primary variable investigated here. Bluelink has produced eddy-resolving 6 day forecasts of the ocean state around Australia since August 2007. The operational system, referred to as the Ocean Model, Analysis and Prediction System (OceanMAPS), has several components, including an ocean general circulation model known as OFAM (the Ocean Forecasting Australia Model), which is nudged over 24 h periods toward analyzed observations generated by the Bluelink Ocean Data Assimilation System (BODAS) [Brassington et al., 2007]. OFAM is based on the Geophysical Fluid Dynamics Laboratory's Modular Ocean Model version 4.0d (MOM4) [Griffies et al., 2007], with some local enhancements to the mixed layer parameterization and insolation. In the OceanMAPS 1.0 version, which is used in the current study, the model domain is global, with 47 vertical levels and eddy-resolving horizontal resolution (0.1°) in the Australian region (90°E–180°E and 16°N–75°S). BODAS [Oke et al., 2005, 2008] combines OFAM output with ocean observations (including sea level from altimetry, SST from satellite radiometry, and vertical temperature and salinity structure from in situ sources such as moorings and Argo floats), generating analyses on a grid with half the horizontal resolution of OFAM (i.e., 0.2° near Australia). BODAS creates analyses via an ensemble optimal interpolation method based on a fixed set of multivariate covariances obtained from a run of OFAM without data assimilation.
 OFAM is initialized in two steps, starting with nudging to a symmetric BODAS analysis at 8 or 9 days behind real time, followed by nudging to an asymmetric analysis (using observations from 5 days before to 1 day after the analysis time) closer to the forecast start time (T + 0). Although the second nudging step has no new altimetry data available to it (but it does use new SST data), the altimetry observations are weighted differently in the first and second nudging steps, according to their ages with respect to the analysis time. The ocean forecast evolving from the initial state is forced by atmospheric fluxes obtained from an operational Numerical Weather Prediction (NWP) system, namely the Bureau of Meteorology's Australian Community Climate and Earth System Simulator—Global (ACCESS-G), Australian Parallel Suite 0 (APS0) implementation [Bureau of Meteorology, 2010]. Although the BODAS-nudged analysis fields are not available at T + 0 (due to the use of a symmetric window), they are available a posteriori for validation purposes. In OceanMAPS 1.0, forecast runs take place twice per week and generate forecasts of daily means of temperature, salinity, SSH, and currents every 24 h out to 6 days (T + 144 h). The current study uses the behind real time, symmetrical analysis data (referred to here as “hindcast data”), since this is the best a posteriori estimate of the ocean state.
 Bluelink grid points used in this study were selected to be close to the coastal tide gauge stations (Figure 1), the observations from which are described in the next section.
2.2. Tide Gauge Data
 Coastal tide gauge data were obtained from the Bureau of Meteorology's National Tidal Centre. The data were collected and made available as part of the “Australian Baseline Sea-Level Monitoring Project”. Data are available for 13 stations around the coast of mainland Australia, 2 stations on the coast of Tasmania, and a sixteenth station at Cocos (Keeling) Island in the equatorial Indian Ocean. The current investigation used “adjusted residuals” data (described in detail below), which are available for 11 of the 13 coastal stations sited on the Australian mainland, but not for the stations at Stony Point or Lorne. The locations of these 13 stations (including Stony Point and Lorne) are shown in Figure 1.
 “Adjusted residuals” data were computed as follows. First, hourly heights of tides were computed from 1 min readings, which were the average of sixty 1-s samples. The highest frequency represented by hourly samples has a period of 2 h; above this Nyquist frequency, the signal will simply be aliased to a lower frequency. To avoid this problem, the hourly data were generated from the 1 min data by filtering out all variability with a period less than 2 h. The hourly data were then converted into the anomaly from the predicted astronomical height of tide. Finally, the isostatic component from atmospheric pressure was removed. These “adjusted residuals” data were used because they can be directly compared to the Bluelink data, which contain neither astronomical tidal contributions, nor an isostatic contribution to SSH.
 This investigation used data from the calendar year 1 January to 31 December 2009. The hourly data supplied by the National Tidal Centre was converted into daily (relative to UTC) mean values. Any days with missing data were excluded from the analysis. The number of days thus excluded were: 1 day for Milner Bay, 3 days for Darwin, 55 days for Broome, 12 days for Hillarys, 1 day for Thevenard, 11 days for Portland, 9 days for Rosslyn Bay, and 35 days for Cape Ferguson. For each day of good data remaining, the 24 hourly readings were averaged to give a single value of mean SSH for that day. Finally, the temporal mean was removed from each station's time series to give a daily mean SSH anomaly.
 In order to isolate the principal CTW frequencies, the Bluelink data were filtered using a fifth-order Butterworth bandpass filter, with frequency cutoffs (−3 dB) at 0.035 and 0.15 cycles per day (cpd). This passes oscillations in the range 28.6–6.7 days. The frequency response of the filter is shown in Figure 2, along with an example of the effect of filtering in the time and frequency domains, using the 2009 time series at Thevenard.
2.4. Correlation Coefficients
 Correlation coefficients (CC) between two sets of gridded, time-dependent variables and were computed as follows [Murphy and Epstein, 1989]:
where s denotes the standard deviation, and angle brackets denote the mean over all grid points.
2.5. Complex Empirical Orthogonal Functions
 CEOFs were computed following the Hilbert transform method of Venegas . A (noncomplex) EOF analysis partitions variability into different modes based on the principal eigenvectors of the covariance matrix. The principal eigenvectors are those associated with the largest eigenvalues. Because the covariance matrix is symmetrical, the eigenvectors are mutually orthogonal. This approach is limited, however, in that it interprets a zero entry in an off-diagonal element of the covariance matrix as a lack of correlation between the grid points represented by the associated row and column. In reality, these two grid points could be perfectly correlated, but 90° or 270° out of phase. The CEOF analysis avoids this problem by additionally considering a second version of the covariance matrix, in which each frequency has been phase-shifted by 90°, hence revealing spatial correlations which would otherwise be masked by being out of phase. The 90° phase shift is achieved using the Hilbert transform. The data are arranged as a complex matrix, where the real part is the original data, and the imaginary part is the Hilbert-transformed data. Each of the real and imaginary parts are standardized by removing the temporal mean and dividing the amplitude at each spatial location by its standard deviation. The current analysis follows the procedure of Venegas  by presenting CEOFs in terms of four main variables: spatial phase angle, spatial amplitude, temporal phase angle, and temporal amplitude. The amount of variance contained in a particular mode is also illustrated by projecting the original data series onto that mode to give a time-varying representation of the mode in the data.
3. Results and Discussion
3.1. Skill of the Bluelink System
 CTWs are readily evident in Hovmöller plots of daily mean sea level from the coastal tide gauge observations and the Bluelink data (Figure 3), as contours aligned from lower left to upper right, indicating SSH anomalies moving along the coast (x axis) with time (y axis). A number of features are evident from these plots. First, it is clear that there are both positive and negative SSH anomalies traveling through the coastal stations, in an anticlockwise direction around the Australian coast. Second, it is evident that in midlatitudes (between Hillarys and Port Kembla), most activity takes place between April and October, which is the Australian autumn, winter, and spring. Third, the largest anomalies are seen to occur between Hillarys and Port Kembla, with the maximum amplitude between Thevenard and Port Stanvac. These observations are consistent with the results reported by Maiwa et al. .
 Although the Bluelink model represents the coastal variability well, the amplitudes of the propagating features are slightly different than in the observational data, being somewhat lower during the first and fourth quarters of the year, and higher in the second and third. This is not surprising, since the tide gauges are located close inshore, often in harbors or on piers, among complex bathymetry, which is not reproduced in the Bluelink bathymetry, with horizontal and vertical resolutions around Australia of 10 km and 10 m, respectively. Furthermore, the tidal observations (Figures 3c and 3d) have had the seasonal cycle removed as part of the process to remove the tidal signal, whereas the seasonal signal has not been removed from the model data (Figures 3a and 3b). For these reasons, rather than comparing the absolute values of SSH between the Bluelink data and the coastal tide gauge observations, the general pattern of variability is compared using correlation coefficients, using the method described in section 2.4 (Figure 4). This comparison reveals a high correlation (CC from 0.633 to 0.903) between the Bluelink hindcast data and the coastal tide gauge data, for the section of coast between Hillarys and Cape Ferguson. The correlations between Bluelink forecasts and the coastal tide gauge data are very similar to the Bluelink hindcast data (Figure 4), which indicates that the Bluelink forecasts capture the CTWs as well as the Bluelink hindcast data. Inspection of the full time series at Thevenard reveals a high degree of correlation (CC of 0.89) between the Bluelink data and the completely independent coastal tide gauge observations (Figure 5).
3.2. Spectrum Analysis
 Having established that the Bluelink data accurately reproduces the SSH variability between Hillarys and Cape Ferguson, it is reasonable to use it as a more complete data set than the coastal tide gauge data, by including data from grid points located between the coastal tide gauge stations. This means that the SSH can be studied continuously around the coast, rather than only at the tide gauge station locations. Bluelink data were extracted in this way for 58 grid points around the coast of Australia, including the 10 grid points corresponding to the coastal tide gauge stations from Hillarys to Cape Ferguson (Figure 1). Furthermore, the Bluelink data set is temporally more complete than the observational data, which have some missing data days at some locations (Figures 3c and 3d).
 Spectrum analysis of this data shows a number of features (Figure 6): The greatest spectral power at the frequencies of interest have an associated period of between 10 and 25 days, with the main peak along the south coast at 10 days; the greatest spectral power is found between Thevenard and Portland; and the spectral power is lower between Portland and Port Kembla. In the northern section of the east coast, the dominant period is found to be at 20 days, with a secondary peak at around 10 days. It is clear that there is a change in the distribution of spectral power with frequency between the south and east coasts, with an evident difference before and after, say, Port Kembla (Figure 6).
3.3. CTW Characteristics Estimated From Filtered Data
 CTW phase speeds are estimated from Hovmöller plots of the filtered, standardized Bluelink data (an example is shown in Figure 7). Note that the standardization process (which is described in section 2.5) reduces the amplitude difference in the original data between the southern and eastern coasts (Figure 3). The Hovmöller plot reveals that phase speeds are higher between Esperance and Portland, at around 9–10 ms−1, than between Stony Point and Rosslyn Bay, at around 2.5–4 ms−1. These speeds are much lower than the phase speed of a Kelvin Wave, which would, for example, propagate at 22 ms−1 where the depth of water is 50 m (typical of the continental shelf depth in the Great Australian Bight), and 20 ms−1 where the depth of water is 40 m (typical of the Bass Strait). On the east coast, these estimates are consistent with phase speeds reported by Maiwa et al.  of 2.1–3.6 ms−1, and other studies cited by them which report speeds of 3–4 ms−1 [Maiwa et al., 2010]. Between Rosslyn Bay and Cape Ferguson, however, the Hovmöller plot indicates that phase speeds are a little higher than this at around 6.2 ms−1.
 An alternative method of estimating the phase speed is to compare the time series at one grid point with time-lagged versions of the time series at a grid point further around the coast. By varying the time lag from zero to a dozen days or more, then calculating the correlation coefficient between the two series, the phase relationship between the two stations can be estimated. This method is somewhat crude, since it averages out phase speed variations between the two stations used, but it is still useful as a gross error check. It is not possible to use this method to measure phase speeds between adjacent tidal stations, because the SSH data are daily averages, but the CTWs may only take a day to travel over such short distances. Using the time series at Esperance and comparing it to the time series at Portland, Port Kembla, and Cape Ferguson, which are progressively further around the coast (Figure 1), averaged over the whole year (Figure 8), the delay required to achieve the greatest correlation is determined as 3, 6, and 10 days, respectively, for the three spatial intervals. This makes sense because, not only does it take progressively longer for the CTWs to travel further around the coast, but also the maximum correlation reduces as the distance between the pairs of locations increases (Figure 8). Given that the distances between the stations are 2268, 3429, and 5368 km, respectively, this corresponds to mean phase speeds between these three pairs of locations of 8.8 ms−1 (Esperance to Portland), 6.6 ms−1 (Esperance to Port Kembla), and 6.2 ms−1 (Esperance to Cape Ferguson). From this, mean phase speeds of 4.5 ms−1 between Portland and Port Kembla, and 5.6 ms−1 between Port Kembla and Cape Ferguson can be inferred. Using the same technique, the phase speed between Hillarys and Esperance (a distance of 1006 km, and a 3 day lag) is estimated as 3.9 ms−1. The phase speeds estimated by this method are consistent with those estimated from the Hovmöller plot.
 Comparison of the standard deviation of the filtered Bluelink SSH data for 2009 and the width of the continental shelf (Figure 9a) shows a clear correlation between the two. The shelf width is taken to be the distance from the coast to the 200 m depth contour, but there are two locations where discretion is applied: first, no value is determined in the Bass Strait, since there is no continental shelf bounding deep water in that location, and second, the value for the shelf width is measured from the shoreline to the closest point of deep water in the vicinity of Rosslyn Bay and Cape Ferguson, where the shelf becomes much wider (Figure 1). There is no evident correlation between the SSH standard deviation and the width of the continental slope, from the shelf break into deep water (not shown). There is also some correlation between the CTW phase speed, as estimated from the Hovmöller diagram (Figure 9b), and wavelength of the first CEOF (Figure 9c), and the shelf width, in that the phase speed is greater and wavelength is longer where the shelf is wider (between Esperance and Portland, and between Rosslyn Bay and Cape Ferguson), but where the shelf is narrower (between Hillarys and Esperance, and between the eastern Bass Strait and a short distance south of Rosslyn Bay), the phase speed is less and the wavelength is shorter. These correlations between the shelf width and SSH standard deviation, phase speed, and wavelength demonstrate that the CTW properties are modulated by the local bathymetry. For this analysis, the wavelength of the first CEOF was estimated from daily plots of the data projected onto the CEOF. On days when the peak amplitude coincides with a particular coastal station, as indicated by the SSH plot touching the spatial amplitude envelope, a half wavelength was measured as the distance between adjacent crossings of the y axis by the SSH plot (SSH anomaly = 0). At the extremities of the plot, a similar method was used, but measuring a quarter wavelength as the distance between the maximum SSH displacement and the adjacent zero crossing. In this way, a number of wavelengths were measured at each station throughout the year. Their means and standard deviations are shown in Figure 9c.
 These results are consistent with the theoretical treatment of Grimshaw , who showed that, for long, nondivergent shelf waves, the amplitude and wavelength increase with increasing shelf width.
3.4. Complex Empirical Orthogonal Function Analysis
 A complex empirical orthogonal function (CEOF) analysis (see section 2.5) of the filtered data shows that the first 4 CEOF modes account for 91.1% of the total variance, and the first 10 CEOF modes account for 98.8% of the total variance. The spatial phase angle of the first CEOF mode (Figure 10a), which accounts for 59.5% of the variance on its own, varies smoothly between Hillarys and Cape Ferguson. The variation in the slope of the plot matches the estimated phase speeds (see section 3.3), since it is somewhat shallower, corresponding to a higher phase speed, between Esperance and Portland, and somewhat steeper on the east coast. The phase plot shows that the first CEOF mode corresponds to a continuous feature propagating along the length of the coast. This propagation can also be seen in the video file of the first CEOF mode (supplied as supporting information). The video plots the filtered, standardized SSH data projected onto the first CEOF and the bounding spatial amplitude of the first CEOF for each day in 2009. The spatial amplitude (Figure 10b) is greater along the south coast than on the east coast, but there are no abrupt changes in amplitude which align with any topographical features, such as the very narrow shelf at Portland, the absent slope into deep water through Bass Strait, or the change of coastal orientation after Hillarys (north-south to east-west) and before Port Kembla (east-west to north-south).
 The first CEOF is particularly strong in early July and early October (Figure 11b). For the early July event, the first CEOF can clearly be seen to be propagating along the entire length of the coast (Figure 12), when plotted at consecutive phase angle intervals identified from the temporal phase angle (Figure 11a).
 Videos of the second mode (17.0% of the variance), third mode (8.3%), and fourth mode (6.2%) are also provided in the supporting information. The second mode is dominated by variability at the extreme ends of the coast, between Hillarys and Esperance in the south-west, and between Port Kembla and Cape Ferguson in the north-east. Anticlockwise propagation is evident from the video. The third mode consists of shorter wavelengths, of around 2000–3000 km, and again the anticlockwise propagation of the wave is evident, as it is also for the fourth mode. A combination of the first four modes and the residual variance not contained within them (i.e., the sum of the remaining 54 modes) shows that the residual is of much lower amplitude than the propagating features. A video, which demonstrates this, is also provided in the supporting information.
3.5. The Role of Wind Forcing
 It is conceivable that the moving SSH anomalies are caused by a direct response of the ocean surface to the changing wind field associated with mobile weather systems, rather than by freely propagating CTWs traveling through the Bass Strait, and from there around the south-east corner of Australia. Inspection of the wind field from mean sea level pressure (MSLP) charts indicates that this may sometimes be the case, but it is certainly not always so. There are also numerous examples where the wind field is conducive to the onshore transport of water in the south-east corner of the continent, but no CTW response is seen in the data. Two specific examples in which the wind field cannot explain the moving SSH anomaly are given here; the first for a positive anomaly, and the second for a negative one. Some comments are then presented on other CTW events during the year, in relation to the associated wind forcing.
 The first case study is from the period 20–28 June, during which time a CTW propagates along the entire length of the coast (see the first case study video in the supporting information). The progress of the CTW on the following dates is as follows: on 20 June, the peak is at Esperance; on 22 June, it is at Port Stanvac; by 23 June, it has passed through the Bass Strait; on 24 June, it is approaching Port Kembla from the south; on 26 June, it is between Port Kembla and Rosslyn Bay; on 27 June, it is at Rosslyn Bay; and on 28 June, it is at Cape Ferguson. Comparison with the MSLP charts, which are shown in the first case study material, but which can be accessed for the whole year on the Bureau of Meteorology's website at http://www.bom.gov.au/australia/charts/archive/index.shtml, shows that, on 20 June, there is a strong westerly wind in the vicinity of Esperance, associated with a complex low pressure system to the south. Ekman transport associated with this wind transports water onto the coast. This process of CTW initiation is consistent with one of the main forcing regions, in the vicinity of Esperance, identified by Maiwa et al. . A low pressure center associated with this system moves into the Great Australian Bight over the next few days, but on 23 June, by which time the CTW peak is already through the Bass Strait, winds are light over the Bass Strait and along the east coast, as indicated by the slack pressure gradient (Figure 13a). The following day, 24 June, when the CTW peak is passing through Port Kembla, there is a slack pressure gradient, associated with light and variable winds, down the entire east coast, across Bass Strait and Tasmania, and for that matter across the Great Australian Bight. The pressure gradient remains slack along the east coast for the period 25–26 June (Figure 13b). A shallow low pressure center forms offshore on 27 June, when the CTW peak is at Rosslyn Bay, but winds remain light in that vicinity until 28 June. Although this sequence of wind forcing is consistent with initiation of the CTW around 20 June, it clearly cannot explain the subsequent propagation of the CTW through the Bass Strait and northward along the east coast.
 The second case study provides a further example where the wind forcing does not explain the transit of the CTW through Bass Strait. It takes place over the period 10–13 September 2009 (see the second case study video in the supporting information). On 10 September, there is a deep and extensive low pressure system well to the south of Esperance, with strong north-westerly winds across the Great Australian Bight, and a weak ridge of high pressure over the Bass Strait. On 11 September, a cold front, with strong north-westerly winds ahead of it (to its east), and west to south-westerly winds behind it (to its west), travels eastward across Bass Strait. Its associated wind field would be expected to force water onto the coast, yet throughout this period, a negative SSH anomaly is traveling through the strait, moving from Portland on 10 September (Figure 13c) to the south-eastern corner of Australia on 11 September (Figure 13d). On 12–13 September, when the negative SSH anomaly is traveling northward up the east coast, the winds in the vicinity are perpendicular to the coast. On 13 September, another pair of cold fronts, and their associated trough, pass through Bass Strait, but the next (positive SSH anomaly) CTW is well to the west, in the vicinity of Thevenard, at this time. Clearly, the wind field is not consistent with either the negative anomaly moving through the Bass Strait, nor with the timing of the following positive anomaly through the strait.
 For the whole of 2009, examples of various relationships between the wind field and the SSH in and around Bass Strait can be found. These include: passages of cold fronts and associated frontal troughs where the associated wind field is favorable to onshore Ekman transport, and therefore to sustaining an SSH anomaly (15–16 January), and which coincide with a CTW transit of the strait; passages of cold fronts and troughs where the wind field is not favorable to the propagation of an SSH anomaly through the strait and/or along the east coast, but a CTW transit is still seen (e.g., 22–23 January, when the wind is perpendicular to the east coast); cold front passages where the wind is conducive to a CTW passage, but no such passage is seen (there are numerous examples of this situation, the best being a period of quiescence in the ocean, when CTW amplitudes are negligible, but a series of cold fronts with associated strong winds transit through the Bass Strait, during the period 2–8 August. Other examples of strong frontal passages with no associated CTWs include 21 August, 3–4 September, and 3–4 December); and the movement of a deep low pressure system through Bass Strait, but with no accompanying CTW (22–23 August).
 Tide gauge observations and numerical model data from the Bluelink ocean forecasting system are used to investigate CTWs along the Australian continental shelf, based on their signature in the SSH field. The close agreement between the model and observational data between the south-west and north-east of the continent justified the use of the model data, which has much greater spatial resolution than the observational data, in this region. CTWs dominated the SSH variability on timescales from a few days to several months.
 The Bluelink data were filtered to isolate the CTW frequencies, whose phase speeds were estimated from Hovmöller diagrams. These phase speeds were 9–10 ms−1 between Esperance and Portland, 2.5–4 ms−1 between Stony Point and Rosslyn Bay, and around 6.2 ms−1 between Rosslyn Bay and Cape Ferguson. On the east coast south of Rosslyn Bay, these estimates were consistent with phase speeds reported by Maiwa et al.  of 2.1–3.6 ms−1, and other studies cited by them which report speeds of 3–4 ms−1 [Maiwa et al., 2010]. They were more specific than the speed of “faster than 4.5 ms−1” reported for the southern coast by Maiwa et al.  and consistent with their range of “3.4–11.3 ms−1 along the western and southern coasts,” determined from their model data [Maiwa et al., 2010]. Using time-lagged correlations between tide gauge station locations, phase speeds were estimated at 3.9 ms−1 between Hillarys and Esperance, 8.8 ms−1 between Esperance and Portland, 4.5 ms−1 between Portland and Port Kembla, and 5.6 ms−1 between Port Kembla and Cape Ferguson.
 Correlations between the width of the continental shelf and of the continental slope (from the shelf break into deep water), and the CTW phase speed, and wavelength, and SSH standard deviation were investigated, and it was found that there is a close correlation between the SSH standard deviation and the width of the continental shelf, but not with the width of the continental slope. CTWs travel faster and have greater wavelengths where the continental shelf is wider. The correlation between the shelf width and SSH standard deviation demonstrated that the CTW amplitude is modulated by the local bathymetry. This is consistent with the theoretical work of Grimshaw .
 A CEOF analysis showed that over 90% of the SSH variance of the filtered data was explained by just four CEOF modes. Over half (59.5%) of the variance was contained in the first CEOF mode, the spatial phase angle of which corresponds closely with the varying phase speeds measured using Hovmöller plots and time-lagged correlations. The spatial amplitude of the first CEOF was greater along the south coast than on the east coast, but there were no abrupt changes in amplitude which align with any specific topographical features, such as the very narrow shelf at Portland, the absent slope into deep water through Bass Strait, or the sharp changes of coastal orientation in the south-west and south-east.
 The role of surface wind forcing was investigated, to determine whether the SSH anomalies moving through Bass Strait and onto the east coast were caused by a direct response of the ocean surface to the changing wind field associated with mobile weather systems, rather than by freely propagating CTWs. Although some examples were found where this could be the case, numerous other situations are found where CTWs propagate through Bass Strait in the absence of favorable wind forcing, and conversely where the wind forcing was favorable but no CTW response was seen.
 We conclude that the majority of the SSH variance seen at CTW frequencies propagates as continuous features between the south-west and north-east corners of the Australian coast, and although modulated in amplitude, phase speed, and wavelength by the shelf width, it is unaffected by the sharply changing coastline orientation, shallow Bass Strait, or wind forcing regions.
 Future work will investigate CTW propagation on the southern continental shelf of Tasmania, which provides an alternative to the Bass Strait as a route to the east coast, and will attempt to detect CTW features along the shelf break. A further area of future investigation will be the change in the distribution of spectral power with frequency between the south and east coasts, which is evident from Figure 6. In investigating the nature of this transfer function, the total volume of the SSH anomaly is expected to prove a more useful measure than the SSH alone, since in this way, changes in CTW shape and propagation speed may be accounted for.
 Other lines of future enquiry are also suggested. The baroclinic nature of CTWs could be investigated through their signature in the current field, for example, using current meter observations. This could be particularly profitable along the Tasman Sea coast, where the East Australian Current might be expected to play a role. The study of a longer time series might also provide insights into the intraseasonal and interannual variability of CTWs, due to seasonal stratification and longer-term variations in the wind field. Extension of the study to the west coast of Australia is also suggested, as is the use of higher-resolution models, which represent the bottom topography in a more detailed manner.
 Bluelink ocean data products were provided by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) and Bureau of Meteorology. Bluelink is a collaboration involving CSIRO, the Commonwealth Bureau of Meteorology, and the Royal Australian Navy. Tide gauge observations were provided by the Bureau of Meteorology's National Tidal Centre, as part of the “Australian Baseline Sea-Level Monitoring Project.” Robert Woodham wishes to gratefully acknowledge the support for this work provided by the Royal Australian Navy, through the “Postgraduate Study at the Australian Defence Force Academy” scheme. Andrew Kiss's (UNSW Canberra) participation in early discussions related to this work is gratefully acknowledged.