Body Tide Correction

Body Tide Correction

The Earth's body tide is modeled as a purely elastic response to the lunar and solar tidal potentials. The algorithm used here is identical to that used for the TOPEX/POSEIDON GDR data, in order to maintain consistency with the ocean-tide models, which by and large depend on T/P data.

The lunar and solar tidal potentials are computed from the semi-numerical expansion of Cartwright & Tayler (Cartwright & Edden, Geophysical Journal of the Royal Astronomical Society, 33, 253-264, 1973), extrapolated linearly to the 1990 epoch. The complete expansion is used, with terms of both second and third degrees in the potential. Only the first term, from the permanent tide, has not been used; by agreement (within the T/P Science Working Group), the permanent tide is included in the geoid model.

The body-tide vertical displacement depends on the adopted h2 and h3 Love numbers. For the T/P project, the following Love numbers were adopted: 

          h2 = 0.609 for all terms of degree 2, except 
             = 0.52  for the K1 tide and its nodal sidelines.
          h3 = 0.291 for all terms of degree 3.

These terms are approximately those computed by Wahr (Geophysical Journal of the Royal Astronomical Society, 64, 677-703, 1981), although, strictly, Wahr found h2 = 0.606 for long-period tides and a much more complex behavior in the diurnal band surrounding the nearly-diurnal free-wobble frequency. Also, all latitude dependence in the Love numbers has been neglected. As noted above, however, we have followed the T/P algorithm for consistency with the ocean-tide models.