17.5 Tidal Prediction
If tides in the ocean were in equilibrium with the tidal potential, tidal prediction would be much easier. Unfortunately, tides are far from equilibrium. The shallow-water wave which is the tide cannot move fast enough to keep up with sun and moon. On the equator, the tide would need to propagate around the world in one day. This requires a wave speed of around 460 m/s, which is only possible in an ocean 22 km deep. In addition, the continents interrupt the propagation of the wave. How to proceed?
We can separate the problem of tidal prediction into two parts. The first deals with the prediction of tides in ports and shallow water where tides can be measured by tide gauges. The second deals with the prediction of tides in the deep ocean where tides cannot be easily measured.
Tidal Prediction for Ports and Shallow Water
The Harmonic Method This is the traditional method, and it is still widely used. The method uses decades of tidal observations from a coastal tide gauge from which the amplitude and phase of each tidal constituent (the tidal harmonics) in the tide-gage record are calculated. The frequencies used in the analysis are specified in advance from the basic frequencies given in Table 17.1.
Despite its simplicity, the technique had disadvantages compared with the response method described below.
The Response Method This method, developed by Munk and Cartwright (1966), calculates the relationship between the observed tide at some point and the tidal potential. The relationship is the spectral admittance between the major tidal constituents and the tidal potential at each station. The admittance is assumed to be a slowly varying function of frequency so that the admittance of the major constituents can be used for determining the response at nearby frequencies. Future tides are calculated by multiplying the tidal potential by the admittance function.
Tidal Prediction for Deep-Water
Several approaches have led to the new knowledge of deep-water tides using altimetry.
Prediction Using Hydrodynamic Theory Purely theoretical calculations of tides are not very accurate, especially because the dissipation of tidal energy is not well known. Nevertheless, theoretical calculations provide insight into processes influencing ocean tides. Several processes must be considered:
Altimetry Plus Response Method Several years of altimeter data from Topex/Poseidon have been used with the response method to calculate deep-sea tides almost everywhere equatorward of 66 (Ma et al., 1994). The altimeter measured sea-surface heights in geocentric coordinates at each point along the subsatellite track every 9.97 days. The temporal sampling aliased the tides into long frequencies, but the aliased periods are precisely known and the tides can be recovered (Parke et al., 1987). Because the tidal record is shorter than 8 years, the altimeter data are used with the response method to obtain predictions for a much longer time.
Recent solutions by ten different groups, have accuracy of ± 2.8cm in deep water (Andersen, Woodworth, and Flather, 1995). Work has begun to improve knowledge of tides in shallow water.
Maps produced by this method show the essential features of the deep-ocean tides (Figure 17.13). The tide consists of a crest that rotates counterclockwise around the ocean basins in the northern hemisphere, and in the opposite direction in the southern hemisphere. Points of minimum amplitude are called amphidromes. Highest tides tend to be along the coast.
Altimetry Plus Numerical Models Altimeter data can be used directly with numerical models of the tides to calculate tides in all areas of the ocean from deep water all the way to the coast. Thus the technique is especially useful for determining tides near coasts and over seafloor features where the altimeter ground track is too widely spaced to sample the tides well in space. Tide models use infinite-element grids similar to the one shown in Figure 15.4. Recent numerical calculations by (LeProvost et al., 1994; LeProvost, Bennett, and Cartwright, 1995) give global tides with ± 2-3 cm accuracy and full spatial resolution.
Further improvements will lead to solutions at the ultimate limits of practical accuracy, which is about ± 1-2 cm. The limit is set by noise from internal waves with tidal frequency, and the small, long-term variations of depth of the ocean. Changing heat content of the ocean produces changes in oceanic topography of a few centimeters, and this changes ever so slightly the velocity of shallow-water waves.
The calculations of dissipation from Topex/Poseidon observations of tides are remarkably close to estimates from lunar-laser ranging, astronomical observations, and ancient eclipse records. Our knowledge of the tides is now sufficiently good that we can begin to use the information to study mixing in the ocean. Remember, mixing drives the abyssal circulation in the ocean as discussed in §13.2 (Munk and Wunsch, 1998). Who would have thought that an understanding of the influence of the ocean on climate would require accurate knowledge of tides?
|Department of Oceanography, Texas A&M University
Robert H. Stewart, firstname.lastname@example.org
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Updated on October 6, 2008