The selection for terms incorporated in the ``background tidal models'' is made in case (2) on the basis of orbital sensitivity analyses where terms having greater than a certain orbit perturbation cutoff are included. Casotto [1989,1991] used an analytical orbit theory to evaluate the ocean tidal perturbations on the TOPEX orbit. On the basis of this study, a set of spherical harmonic coefficients spanning over 80 tide lines was identified as being TOPEX-sensitive. Because of the large number of tidal terms required, Oscar Colombo [1989, unpublished notes] developed an efficient algorithm to evaluate these tidal models based on a linear scaling of tidal admittances as summarized in Nerem et al., [1993a]. By increasing the number of harmonic coefficients in both the static and tidal gravity models, the omission error on lower orbiting satellites is minimized.
In light of the extensive improvements in orbit accuracy achieved
on T/P and the improved ocean tidal models resulting from an analysis
of its altimetry [ Eanes, 1994; Pavlis et al., 1994;
Schrama and Ray, 1994; Ray, Sanchez and Cartwright , 1994], the
tide modeling problem has been recently revisited. Marshall et al.,
[1994c], by evaluating the spatial and temporal distribution of radial
errors on the T/P orbit, observed a geographically dependent signal
with a 60-day period which they attributed to mismodeled shorter
wavelength tides. This 60-day period closely matches the aliasing
period of the principal semi-diurnal lunar and solar tides (M
and S
) on T/P. Bettadpur and Eanes [1994] showed that a
significant improvement (
1 centimeter RMS) in T/P radial orbit
knowledge can be achieved through incorporation of more complete and
accurate background tide models.
The neglect of atmospheric tidal modeling in orbit
determination, especially at the solar diurnal (S
) frequency, is
an area now receiving significant attention. Nerem et al., [1994b]
proposed that an anomalous variation seen in the evolution of
the eccentricity of the Lageos orbit in part arises from ignoring
these tidal effects. The S
and S
atmospheric tides give rise
to dominating long period orbital perturbations on LAGEOS of 561 and
365 days respectively. These correspond to the spectral peaks seen in
the in-phase component of Lageos' one-cycle-per-revolution
anomalous acceleration discussed in Eanes and Watkins [1991],
Nerem et al., [1993b] and Gegout and Cazenave [1993].
However, surface forces, like those described later, are still not
ruled out as a possible explanation.