How harmonic constituents help us predict tides
How is it that tides can be predicted so far ahead? The tide is made up of lots of simple constituents which are basically just sine waves of differing frequency, amplitude and phase. For each astronomical cycle, there is one or more of these ‘waves’ to describe its affect on the water. These waves are called harmonic constituents.
These harmonics are given short names – the four most common (and generally most influential on the tide) being M2, S2, 01 and K1. Each harmonic constituent is tied in to a particular astronomical cycle and therefore has a fixed frequency (usually specified in degrees per hour)
irrespective of the location. The amplitude and phase (time lag) of each constituent varies depending on the location. Each amplitude / phase pair of values is called a harmonic constant.
The most significant harmonic constituent is M2 – the twice daily tide generated by the moon. It has a frequency of 28.9841°/hour and hence is slightly slower than S2. Whereas S2 completes a 360° cycle in exactly 12 hours, M2 takes approximately 12 hours and 25 minutes. This is why consecutive high waters occur at roughly this interval.
For the port of Minehead, M2 has an amplitude of 3.61m and a phase of 179°. Avonmouth, which is about 40 miles up the estuary, has an M2 amplitude of 4.29m and a phase of 200°. This means the M2 tide is 68cm greater and arrives 21° (or about 43 minutes) later. S2, the twice a day tide generated by the sun, is usually the second most significant constituent. Based on the theoretical equilibrium tide, it is about 46% the size of M2, although for UK waters it is usually more like 35% of M2. It has a frequency of exactly 30°/hour (a period of 12 hours).
Predicting the tide is simply a case of adding the effects of the individual harmonic constituents at a particular point in time, something that can be done easily and quickly on a computers.
How the harmonic constants are worked out is the next obvious question. The starting point is always a time series of water levels or currents – whether they are from a tide gauge, a current meter or synthesised from a numerical computer model.
The most popular way, and the method used for producing the harmonics for major ports, is to start with a time series of observations from a tide gauge. By analysing this observed data and looking for a strong signal in the frequency spectrum at the fixed frequencies of the harmonic constituents, an amplitude and phase can be computed for each specific to the location of the observations.
For tidal currents, there needs to be 2 sets of harmonic constants for each location, one for the east component of the current and the other for the north component. Once the predictions for these two components have been made, they can be combined to give an overall current speed and direction at the location.