Tides have been studied for longer than most other ocean phenomena; however, for most of this time, the only measurements possible were those made by tide gauges on the coasts, mostly in harbours, which were thus subject to local factors, the geometry of the coasts and, in particular, the bathymetry. Now, satellite altimetry provides measurements of sea surface heights in the open ocean accurate to 2-3 centimetres that are assimilated into mathematical tide prediction models. This has helped to improve tide models (now accurate to within 2 cm in the open ocean), and increase our understanding of Earth-Moon interactions such as the Moon’s impact on the length of the day on Earth. In return, tide models are used to remove tidal effects from altimetry data.
Amplitude of the M2 tidal constituent (in centimetres) derived from the FES99 model. Cotidal lines indicating the phase every 30 degrees originate at amphidromic points where the tidal range is zero.
Amplitude of the lunar wave for a period of 6 hours (wave M4) in the particularly complex areas of the North Sea and English Channel. A long series of altimetry data, from Topex/Poseidon and then Jason-1, should make it possible to significantly improve forecasting.
The combined attraction of the Moon and the Sun generates tides on Earth. Calculating their effects is not as easy as it might seem, as the distance and inclination of the Sun and Moon with respect to Earth, and with respect to each other, have to be factored in. The shape and size of ocean basins is another factor that makes predicting tides such a complex matter. In order to calculate tides, they have to be broken down into sinusoidal waves of given periods, each of which varies in amplitude and represents one component of the problem. Thus, one of the waves, called M2, is due to the attraction of a ‘virtual’ Moon placed on a perfectly circular orbit in the Earth’s equatorial plane. It has two high and two low tides per day (semi-diurnal wave). The K1 wave, with a diurnal period, reflects declination variations of the Moon and Sun. The amplitude of the tide at a given time and place is the sum of all these sinusoidal waves. In certain areas, a hundred of these waves have to be added together to obtain a precise forecast.
One of the questions that needs solving when using altimetry in tidal studies is the issue of aliasing. Depending on the satellite’s repeat period, some tidal constituents are always seen at the same point in their cycle, and thus have not been accurately measured (this is especially true for sun-synchronous satellites, which see semi-diurnal tidal constituents as stationary), whereas other tidal constituents with periods shorter than the satellite’s are measured with sparse sampling with respect to their duration, and are thus difficult to piece together.
In addition to their direct effects on maritime and coastal activities, tides appear to have a less well-known impact on the Earth’s climate. This discovery, which is based on almost ten years of highly precise altimetry data, has led to a new understanding of the way in which the Moon influences our planet. Ocean waters are stratified according to their density. The different layers mix with difficulty. However the tidal currents coming into contact with the relief of the ocean bottom (even if this is very deep) create waves which are propagated at the interface between two layers of different density (internal waves). It is currently thought that this mechanism contributes more than half of the vertical mixing of water masses. This mixing is fundamental to large-scale ocean circulation (thermohaline circulation) which enables the redistribution of heat from the equator to the poles.
Energy flow of the semi-diurnal, lunar tidal wave (M2). The illustration shows the displacement of energy from areas in which it was generated towards dissipation areas. It has been demonstrated, for instance, that the energy dissipated on the Patagonian shelf (to the east of South America), one of the areas where tides are highest, comes from the Pacific and that 40% of the total energy contributed by the Earth/Moon system to ocean tides, is dissipated in the North Atlantic.
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