Choose your region on the map above, then the day on the calendar, then click Mouse over the observation sites to see detailed information. For current meters this includes the magnitude and direction of the observation-based predicted tidal current, the rms magnitude of sub-tidal variability measured by that current meter and the magnitude and direction of the observed mean current. Clicking the observation sites takes you to month-per-page graphs of observation-based predictions compared with the model-based predictions. |

Month-per-page graphs | |
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For each current meter or tidegauge, these graphs compare the observation-based tidal predictions ('o' for short) with co-located model-based tidal predictions ('m'). The current velocities are shown as speed and direction, and components along East, North and the major and minor axes of the observed M2 tidal ellipse. The agreement of o and m is characterised by listing rms values of each separately, as well as of the model error m-o. For currents this is done for the scalar components as well as for the vector difference. If the vector error can be minimised by lagging the model details are given. The direction error is characterised by listing the 25th, 50th and 75th percentiles. The [PREV] and [NEXT] links step a month at a time in 2019, or back to when actual observations can be included on the graph (1983 in some cases). Browsing the graphs with actual observations reveals how Australia's ocean currents range from tidally-dominated (e.g. in Bass Strait as shown at right), to mixed (e.g. Palm Passage) to non-tidal, such as off Bateman's Bay. |

Aggregate error statistics | |
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These plots summarise the comparisons of observation-based and model-based predictions of the tidal component of sea level (upper) and currents (lower). Black dots show modelled vs observed rms amplitude. If these are on the dotted line it means the modelled amplitude is the same as observed (but not necessarily the phase). Red dots show model-observation difference vs observed amplitude. If these lie along the zero line it means the observed and modelled phase and direction also agree. The sites with the largest observed amplitudes, or largest model-observation differences are named, and discussed below. The inset tables list 3 statistics (the mean, median and 95th percentile across the listed number of locations) of 4 quantities; 1) the rms modelled sea level or current, 2) the rms observation-based sea level or current, 3) the rms (vector in the case of velocity) difference of the model and observation-based estimates, and 4) the difference of the modelled and observed rms values. |

**55 IMOS ADCPs;**these Acoustic Doppler Current Profilers were deployed by or have been contributed to IMOS. These observations can be assumed to be quite accurate. Here, we use the depth-average of the observations, which span the whole water column except for a few m at the bottom, and the surface-most 15%.**13 CSIRO current meters;**selected from the CSIRO collection for being in locations (Bass Strait, NW shelf and Gulf of Carpentaria) where tidal currents are significant. These non-ADCP moorings included either one or two current meters. In the case of two, we have simply averaged the observations for the record segments when both were operating. [plots of the individual intrument records, their average and the tidal fit]**10 UNSW Aanderaas:**Middleton et al. (1984) and Griffin et al. (1987) studied the anomalous tides of the Southern Great Barrier Reef using these observations made by single, mechanical RCM4 Aanderaa current meters. By modern standards, these instruments are not very accurate. Firstly, the flow direction is only sampled once an hour, so short-period changes of direction are not averaged. To minimise noise due to waves, the instruments were moored fairly low in the water column, at the risk of under-estimating the depth-average velocity. Some had to be deployed close to islands, with the result that they recorded effects (such as asymetric ebb and flood directions) that the model is unlikely to be able to reproduce due to its imperfect representation of topography. Flood-ebb asymmetries may not be well represented by a sum of harmonic tidal constituents, either. The instrument deployed west of Bugatti Reef, for example, has one of the highest rms vector differences from the model. This can be seen to be mostly due to persistent offsets between the observed flow direction and both the modelled and tidal-fit flow directions. The situation with the Tern Island meter is slightly different. Here, the observed flood tide is to the SSW, but the ebb was more likely to be either to the ENE or NW instead of NNE, as shown in the hodograph at right (click to enlarge). Neither the tidal self-prediction nor the model represent this. The impeller of the Creal Reef meter appears to be intermittently obstructed, so the tidal prediction there is probably not accurate, explaining the large discrepancy from the model.-
**4 ARENA ADCPs:**These were deployed in Banks Strait by the University of Tasmania as part of AUSTEn, to assess the renewable energy potential of the strong currents there (Wijeratne et al. 2012).

We have used the UTide tidal analysis software of Codiga (2011) to compute amplitudes and phases for up to 8 (depending on the record length) semi-diurnal and diurnal (M2 S2 N2 K2 O1 K1 P1 and Q1) tidal velocity constituents (details for IMOS sites), allowing predictions to then be made for any chosen period.

In contrast to the situation with tidal currents, predictions of tidal sea level are already widely available and heavily used. We obtained tide gauge data from

- 44 locations from the National Operations Centre (NOC) Tidal Unit of the Bureau of Meteorology. Some of these data sets are many years long. We have used just 1 year (a recent full year) from each location.
- 64 from a compilation by Pringle (2017) (consisting only of harmonic constants, not timeseries, so we can not show any of the actual data)
- 9 from the UNSW SGBR data set.

**Modelled tidal sea level and currents**

The Oregon State University Tidal Prediction Software (OTPS) (Egbert and Erofeeva, 2002) provides estimates of the 8 tidal constituents listed above on a 1/12° (latitude and longitude) grid, for the sea level and the depth-averaged current velocity. This system uses the TPXO9 tidal model, which assimilates satellite altimeter measurements of sea level to make it as accurate as possible. We use the TTide software (Powlowicz et al 2002) to produce estimates of the semidiurnal and diurnal tidal sea level and current velocity. When comparing this model with observations, we assume that the product of water depth and velocity is more accurate than velocity alone, so we estimate velocity as model transport (model depth times model depth-average velocity) divided by the observed depth at the location of the current meter. When showing maps of model velocity, we simply divide the model transport by model depth at each grid point. The comparisons of this model with the observation-based predictions shows that its simulation is quite accurate - except for a few regions (King Sound, Gulf St Vincent) where there is a local maximum. Gauges at Karrakatta Bay, King Sound, Androssan and Port Stanvac identify these discrepancies).

There are two main reasons why there are not presently many 'official predictions' of tidal currents to accompany the predictions of tidal height published, for example, by the BoM (see the 'Tidal streams' button).

- the tidal component of the current is weaker than (or comparable to) the non-tidal components of the current for much of Australia's marine estate (i.e. nearly everywhere south of 25°S). Our index map shows the locations of available current meters, colour-coded by whether tidal currents are dominant, comparable or weaker than non-tidal currents. It is only at 33 of the 82 locations sampled that tidal currents are dominant, and another 19 where they are comparable. For sea level, in contrast, there are few places where the amplitude of non-tidal variability is comparable to, let alone exceeds, the amplitude of tidal variability.
- tidal currents are intrinsically more complex - varying markedly over short distances in line with the sea floor topography, as you can see by toggling between the maps of sea level and speed. This is why the rms error (8cm/s average across all sites) of the tidal model's velocity is about 50% of the tidal currents, while the error of the sea level (14cm averaged across all sites, as also reported by Haigh et al. 2014 using a different model) is only 20% of the signal.

Models like eReefs simulate both tidal and non-tidal currents, and similar models are also being constructed for other regions around Australia. Regardless of these developments, however, we think there is value in publishing predictions of the tidal component of the currents without attempting to include the non-tidal component. For this first version of the website, we have used the OTPS tidal modelling system and the relatively sparse array of observations-based predictions. We hope to obtain other existing observations, and that a regional tidal model under development at CSIRO as part of AUSTEn will agree even more closely with the observations than the global tidal models do.

**tide** The term 'tide' is sometimes used to describe any variation of the sea level or the current. Here, we use the oceanographer's definition, which is that the tide is the astronomically forced variation of sea level and current. Hence, and in contrast to the non-tidal variability in the ocean, the tides are equally predictable for any period in the future (or the past), because the tidal forcing is precisely linked to the orbit and rotation of the Earth and the orbit of the moon.

**tidal prediction** The most accurate way to predict the tides (currents or sea level) at a certain location is to obtain a record of the tides for a period then do what is known as a tidal analysis to determine the amplitudes and phases of all the tidal constituents, then a prediction, which is the reverse operation. We have used the TTide and UTide matlab software for this. To make a prediction for a location where no observations exist, one has to use a tidal model, such as TPXO9 or FES2014. This is because the ocean's response to the tidal forcing is very complicated, due to the complex shape of the oceans, coastal seas and continental shelves. Local resonances can increase the amplitude of the tides in some places, while destructive interference can reduce it elsewhere. These dynamics are frequency-dependent, affecting the diurnal and semi-diurnal tides differently. The relationship of currents to heights is also complex. Strong tidal currents do tend to occur in regions with high tidal sea level amplitudes, but at some distance away from where the range is greatest, and not always at the time you might expect.

**tidal constituent** For most locations, the dominant tidal constituent is M2. This measures the amplitude of the sealevel perturbations towards the moon on one side of the earth, and away from it on the other. Taking the rotation of the earth and the orbit of the moon into account, this constituent has a period of 12h 25min 14.4s. The dominant constituent associated with the sun is called S2, and has a period of exactly 12h. The 50.5 minutes-per-day difference of these two periodic signals is what gives us the 28.5d spring-neap cycle of the daily tidal range (and the waxing and waning of the moon). There are 145 named tidal constituents, together accounting for the complex but periodic cycle of the tides.

**tidal ellipse** Being a vector (two dimensional) quantity, tidal currents are more difficult to describe than tidal sea level. For each tidal constituent, the tidal current velocity vector traces out an ellipse. It is only in narrow channels that the current goes simply back and forth. In some places, the ellipse is close to a circle, with the speed of the current remaining constant, and only the direction changing. More commonly, the amplitude of the major axis is significantly greater than the amplitude of the minor axis. The bearing of the major axis is commonly referred to as the direction of the flooding tide.

**diurnal and semi-diurnal** Diurnal tidal constituents (e.g. O1, K1) have periods near 24-25h. They are smaller than the semi-diurnal (near 12h) constituents in most places, the SA Gulfs being a notable exception, where the K1 currents are stronger than the M2 currents. They are caused by the asymmetry of the sea level perturbations on the near and far sides of the Earth.

**long-period tides** These are constituents with periods near 15d, 30d, 6 months and 12 months. Some are due to direct astronomical forcing (i.e. non-colinearity of orbital axes, eccentric orbits, etc) while others are due to the non-linearity of the ocean response to the astronomical forcing. Neither sort of long-period tide are included in the predictions shown here. They are small compared to the errors of the short-period tides.

**non-tidal variability** Broadly speaking, this refers to the many other causes of ocean currents and sea level changes, such as wind, atmospheric pressure, heat gain or loss, freshwater gain or loss and eddies at a wide range of sizes. There are, however, a few grey areas. Tidal currents rushing past a headland may spin up an eddy, depending on the state of the spring neap cycle or the existence of a large-scale alongshore current. That eddy is clearly caused by the tide, but it is unpredictable. Conversely, the regular daily cycle of winds and temperature, modulated on the annual timescale, also causes a fairly predictable signal in observations of the ocean, which tidal analysis software inevitably includes in its estimation of some of the diurnal and annual tidal constituents.

**sub-tidal variability** is due solely to physical processes operating at time scales longer than a day or so (i.e. excluding semi-diurnal and diurnal tides). We estimate the rms amplitude of these by applying a Hanning filter to the observations with a half-amplitude width of 20h. This filtering removes all semi-diurnal variability, not just the phase-locked components at resolvable frequencies. From the prediction point of view, the historical amplitude of sub-tidal variability is an estimate of prediction error, since the actual sub-tidal variability can only be predicted close to real time using weather and other data.

**internal tides** In some places, currents associated with the internal tide rival or exceed those due to the barotropic ('normal') tide. These are presently out-of-scope for this website but remain an active area of research because of their importance to everything from climate modelling (because they do vertical mixing and dissipate energy) to offshore engineering (e.g. on the NW shelf). Internal tides occur when the barotropic tide excites wavelike motions of the layers of the ocean with different density. If the amplitude of these waves is large, tidal-period velocities in the upper and lower layers can be in the opposite direction. Internal tides come and go depending on the stratification of the ocean, so they are harder to predict than the barotropic tide.

**rms** Root mean square, i.e. sqrt(mean(x^2)) where x comprises N estimates of some quantity (or a difference of two comparable quantities), either scalar (e.g. sea level) or vector (velocity, as u + iv). Here, all quantities considered are tidal predictions, which have zero mean over the time intervals considered. In the case of velocities, the rms values are vectors, only the magnitudes of which are used unless specified otherwise.

- Codiga, D.L., 2011. Unified Tidal Analysis and Prediction Using the UTide Matlab Functions. Technical Report 2011-01. Graduate School of Oceanography, University of Rhode Island, Narragansett, RI. 59pp. ftp://www.po.gso.uri.edu/pub/downloads/codiga/pubs/2011Codiga-UTide-Report.pdf
- Egbert, G.D. and S.Y. Erofeeva, 2002: Efficient Inverse Modeling of Barotropic Ocean Tides. J. Atmos. Oceanic Technol., 19, 183–204, DOI
- Haigh, I.D., Wijeratne, E.M.S., MacPherson, L.R., Pattiaratchi, C.B., Mason, M.S., Crompton, R.P., George, S., 2014. Estimating present day extreme total water level exceedance probabilities around the coastline of Australia: tides, extra-tropical storm surges and mean sea level. Climate Dynamics, 42, 121-138. DOI
- Griffin, D.A., Middleton, J.H. and Bode, L. (1987). The tidal and longer period circulation of Capricornia, southern Great Barrier Reef. Aust. J. Mar. Freshw. Res., 38, 461-474.
- Middleton, J.H., Buchwald V.T. and Huthnance, J.M. (1984). The anomalous tides near Broad Sound. Continental Shelf Research 3, 359-381.
- Pawlowicz, R. B. Beardsley, and S. Lentz, "Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE", Computers and Geosciences 28 (2002), 929-937.
- Pringle, William (2017),Major tidal constituents for the Indian Ocean and Western Pacific Basin, Mendeley Data, v1 http://dx.doi.org/10.17632/tjyjn56jbf.1
- Wijeratne, E. M. S.; Pattiaratchi, C. B.; Eliot, Matt; Haigh, Ivan D. (2012). Tidal characteristics in Bass Strait, south-east Australia. Estuarine, Coastal and Shelf Science, Volume 114, p. 156-165.DOI

- Australian Tidal Energy - AUSTEn
- Oregon State University Tidal Data Inversion (for details about OTPS and TPXO9).
- FES2014
- Assessment_of_the_FES2014_Tidal_Currents_on_the_shelves_around_Australia
- T-Tide
- UTide
- anyTide

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