Tidal potential

The tidal potential Oq can be composed with sufficient accuracy from,for example, two parts each of the sun and moon Of, = Although hn/ would be even... 

The development of the tidal potential of the moon and sun is given, for example, by Bartels and Hom (1952). The potential is expressed in a geocentric coordinate system and depends on the location (2, tp) and on the time-dependent quantities distance r, declination <5 and right ascension a. 

The orbit of the moon is particularly complicated. As the tidal potential in this study is... 

The tidal acceleration at any point on earth at any point in time can be computed from the tidal potential. This is either done analytically (Bartels, 1957) or via finite-difference approximation -AO/(/ cos (p A2) or -A/( / Ageographic latitude is crucial in this context. A water particle at the equator is clearly subject to alternating acceleration because the acceleration vector twice points east, and twice west. At 20°E, 59°N, that is, in the middle of the Baltic Sea, the vector points predominantly in southerly directions. The asymmetric picture at the Baltic Sea location results from the latitude dependent terms in (7.18) and (7.19), which cause the equipotential surface to be lowered by an average 19 cm at the poles, and to be raised by about 10cm at the equator (Torge, 2003). Near the north Pole, the amounts of tidal acceleration decrease strongly and there remains a purely diurnal fluctuation. 

Hartmann, T., Wenzel, H.-G., 1995. The HW95 tidal potential catalogue. Geophysical Research Letters, 22, 2553-2556. 

Since this is a conservative force field it can be represented by the gradient of a scalar potential, the tidal potential Vgid... 

Prescribing Vtid (0) = 0 the tidal potential is uniquely determined ... 

The development with respect to Legendre polynomials Pn(cos %) is convergent for r < rm this condition is always met in the vicinity of the earth. Restricting to the main terms of degree n=2 Laplace s representation of the tidal potential is obtained... 

In the present context it is reasonable and sufficient from the practical point of view to base the representation of the radial and tangential displacements of the earth s surface on the Love—Shida hypothesis. In this approach introduced by Love (1909) and Shida (1912) the radial displacement Ar and the tangential displacement components Ax (north-south direction) and Ay (east—west direction) are parameterized by the tidal potential and the Love-Shida numbers h, 1 ... 

In establishing practical procedures for tidal reductions of levellings and ellipsoidal height differences observed by GPS the choice of the quasi-stationary state ("zero" or "mean" state) is decisive. Another feature of the reduction procedure concerns the type of representation of the tidal potential, i. e. either Laplace s tidal formula (6) or the harmonic development (8). In the folowing the resulting four alternatives are presented. 

Special attention has been given to the treatment of the permanent MqSo term in the harmonic development of the tidal potential. It is obvious that the choice of the quasi-stationary model — either the "zero" or the "mean" state — is decisive. The "zero" case is to be preferred from the point of view of Physical Geodesy while the "mean" case shows some advantages for hydrographical or oceanographic applications. The difference between the tidal reduction values for precise levellings corresponding to the "zero"... 

A few words are now in order about tidal deformations. They are caused by the moon and sun gravitational attraction (see Fig. 13). Tidal potential caused by the next most influential celestial body, Venus, amounts to only 0.036% of the luni-solar potential in practice only the luni-solar tidal potential is considered. The tidal potential of the... 

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