TIDE DECOMPOSITION AND PREDICTION

A very simple theory explaining the tides on an Earth covered completely by water of uniform depth shows that at a point on the equator, the Moon and Sun would raise the sea level by 54 and 24 cm, respectively. This suggests that, as a rule, one may expect the lunar tide to be about twice as large as the solar tide, and this applies at many locations in the world.

In general, when studying variations in tidal levels at a location, it is possible to decompose them into harmonic components with specific periods, A harmonic component has the form of a sine wave with a definite period and amplitude. The different waves may begin at any instant and are disposed differently in time with respect to each other from place to place. By convention, the delay of a component wave at 0000 hours Greenwich Mean Time (GMT) on 1. January 1900 is the measure by which individual tidal constituents at a location and constituents of the same type at different locations are positioned in time with respect to each other.

Since the creation of tidal theory, different component waves have been denoted by selected symbols. Only the four components: M2 with the period of 12.42 hrs, S2 with the period of 12.00 hrs, K1 with the period of 23.93 hrs and O1 with the period of 25.82 hrs, will be referred to here, since they yield an adequate qualitative description of Australia's tides. Since their subscripts refer to the number of cycles per day, 1 and 2 denote diurnal and semi-diurnal waves, respectively.

The speed of a harmonic component is the number of degrees per mean solar hour, i.e., 360ş, divided by the period under consideration. The speeds per hour of the components above are:

M2 : 28.98ş, S2: 30.00ş, K1 : 15.04ş, O1: 13.94ş

With this convention, the tide at any location may be represented as the sum of four waves with the above periods and displaced in time in a known manner on 1. January,1900. One does not state the displacements of these waves in terms of hours, but in terms of phase angles, using the conversion formula:


Phase angle = delay time x speed.

The general expression for any one harmonic component now becomes:

Height of tidal component = amplitude x sine (speed x time-phase angle,

where amplitudes are given in centimetres and times in hours.

The process of decomposition of tides into components is called harmonic analysis and the components harmonic constituents.

The local datum of a tide gauge and of navigational charts is also of importance. They are not always identical. In Australian waters, it is common practice to use as a chart datum a level for which the tide never has negative values. This objective is almost achieved by subtracting from the mean sea level, the value of tidal heights averaged over a longer period, the sum of the amplitudes of the four harmonic constituents M2, S2, K1 and O1, a quantity which is referred to as Indian Spring Low Water (ISLW) and stresses the importance of the above constituents. Nevertheless, negative tidal heights occur at many locations around the Australian coast.

The tidal range at a location is twice the sum of the amplitudes of all tidal components, since at some time or other all of them are superimposed. The difference between the theoretical and observed tidal ranges varies around the coast. In the south-west, it reaches its maximum, because meteorological tides dominate there.

The character of tidal sea level variations changes along Australia's coast as a result of the interaction of the tidal wave, coming from the deep ocean, with the continental shelf. One possible classification of tide types is based on the ratio

amplitude (K1) + amplitude (O1)

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amplitude (M2) + amplitude (S2)

of the sums of the principal diurnal and semi-diurnal tidal ranges. One speaks then, by convention, of a semi-diurnal tide when this ratio lies between 0 and 0.25, of a semi-diurnal tide with diurnal inequalities when it lies between 0.25 and 1.5, of a mixed tide when it lies between 1.5 and 3.0, and of a diurnal tide when it exceeds 3.0. A comparison of the tide types with actual tide curves explains the significance of the terms semi-diurnal, diurnally unequal, mixed and diurnal.

In practice, the decomposition of a tide record into its harmonic constituents is achieved mathematically by reduction to its minimum of the sum of the differences of the observed and the approximating decomposed values over a selected time period. This method of least squares has proved to be very useful in many areas of applied science and has been greatly simplified by the modern computer.

Tide prediction employs the harmonic constituents to compute the sum of simple waves with appropriate amplitudes, phases and periods. As a rule, tide predictions are confined to the determination of the times of daily high and low waters. However, complicated shipping conditions. as they occur, for example, in Torres Strait and at entrances to major harbours, may justify preparation of tables of hourly tidal heights.

The Australian National Tide Tables, published by the Hydrographer of the Royal Australian Navy, contain about 70 sets of predictions of high and low waters and of their times of occurrence for ports of the Australian Coast and Papua New Guinea. They also present predictions of the tidal currents in Torres Strait and list the above mentioned four harmonic constituents, based on available periods of observation.