3.1.5.2. Semidiurnal/Diurnal Tides

Diurnal and semidiurnal ocean tides cause orbital perturbations, which alias into the same part of the spectrum as the effects from the more interesting non-tidal signals of paramount importance to this investigation. Recent progress in the determination of the ocean tides from analysis of TOPEX/Poseidon (T/P) altimetry has generated ocean tide models with accuracies at the few centimeter level in the deep ocean [Ma et al., 1994; Eanes and Bettadpur, 1994; Shum et al., 1995]. These advances provide a good dynamical ocean tide model to use in this investigation [Eanes and Bettadpur, 1994]. We have found that only the largest terms in the tidal potential need to be readjusted using the SLR data, and these signals are most likely due to errors in the models of the solid Earth's response to the tidal forcing, especially at the low-frequency 18.6-year tide. The exceptions are the solar semiannual and semidiurnal frequencies which contain significant non-tidal contributions.

3.1.5.3. Intraseasonal, Seasonal, Semiannual, Annual and Interannual Variations

The observed satellite excitations constitute a record of the zonally averaged mass distribution of the planet. As a result they can be used to study the natural variability of the seasonal cycle over the last 19 years. In the context of this investigation, one of the most important signals in the orbital excitations is the annual variation, which is mostly due to mass redistribution in the atmosphere and oceans driven by solar energy input and the ground water circulation and ice/snow accumulation or melting. The variability of this annual signal from year to year may be one of the best indicators we have of the global effects of climate change for decade time scales. In addition, interannual variations exist (e.g., ENSO) that are related to longer term interactions between the atmosphere and ocean.

Each well-tracked satellite provides a unique constraint on a linear combination of the zonal harmonics, dominated by $J$2, and referred to as the "effective $J$2." We have computed predicted orbital excitations from the zonal harmonics of the atmosphere mass discussed in Chao and Au [1990] and have compared them to the observed orbital excitations from Lageos-1 and Starlette. Variations near the annual frequency were isolated using complex demodulation. Two versions of the predicted excitations were formed, one using the inverted barometer (IB) model for the ocean's response, and one treating the oceans as rigid (non-IB). The variability of the annual amplitude and phase in the observed excitations was found to fall between those of the IB and non-IB extremes.

An effort to quantify the role of the oceans and ground water in this balance will be a primary thrust of future efforts. Cheng et al. [1994] reported results of using the mean annual ground water contribution from Chao and O'Connor [1988] and a new result computed using monthly precipitation and surface temperatures from NCAR for over 3900 stations based on a procedure described in Lei and Gao [1992]. The use of the new ground water result generally improved the agreement between predictions and the satellite constraints.

We have begun the analysis of ocean-bottom pressure output from the coupled ocean/atmosphere model of Ponte [1995a,b]. Comparison of this time series to the orbital excitations could result in improved correlations over those using the IB/non-IB approximations to the oceans response to the atmospheric pressure loading. In the future, comparisons will be made to output from the Semtner-Chervin [1992] ocean model. In addition, interannual variations (e.g., ENSO) exist that are related to longer term interactions between the atmosphere and ocean. Direct observation of the orbital effects of these signals and those in the EOP provide useful new information on the mechanisms causing these effects.

A recent paper by Chao and Eanes [1995] studies the seasonal and intraseasonal variations in the orbit of Lageos-1 and its explanation in terms of the mass redistribution in the atmosphere. The more accurate separation of tidal and non-tidal signals now possible using the new T/P ocean tide models has recently improved the analysis in this paper. Figure 7 shows a comparison of the power spectrum of the Lageos-1 excitations to the atmospheric predictions [Eanes and Bettadpur, 1995] using the Chao and Au [1991] time series of atmospheric zonal harmonics. A similar comparison has been made for a lower altitude geodetic satellite, Starlette [Eanes and Bettadpur, 1995]. The observed excitations are bracketed by the IB and non-IB predictions, but except near the annual band the agreement is better with the IB version of the predictions. The coherence spectrum (not shown) indicates significant correlations up to frequencies of 6 cycles per year, and the correlation is generally higher for the IB version of the prediction. As discussed above, ground water and ocean mass redistribution is required near the annual period to close the comparison of observed and predicted results.

In our study, the GCM output provided by the European Centre for Medium Range Weather Forecasts (ECMWF) and U.S. National Meteorological Center (NMC) are used to compute mass redistribution models from the atmosphere, and the NCAR data set of monthly precipitation and surface temperature for over 3900 stations and a procedure described by Lei and Gao [1992] are used to develop a new model for global surface water variations [Cheng et al., 1994]. Comparison of second degree annual variation from our water mass redistribution model [Cheng et al., 1994] agrees well with the model from Chao and O'Connor [1988]; however, the amplitude of the third degree annual variation in our model is only half of that given by Chao et al. [1988], and the phase difference is very large at about 180°. Detailed analysis of the discrepancy is underway.

Detailed comparisons of modeled geophysical and meteorological effects (atmosphere and ground water) in $J$2 and $J$3 variations with satellite-observed variations (Ajisai and Starlette) indicate that the contribution of atmospheric excitation is approximately 30%-70% for Starlette, and approximately 40%-80% for Ajisai, for the annual variations [Cheng et al., 1994, 1995]. The contribution of ground water variations is smaller. As expected, annual variations are larger than semiannual variations. A significant percentage of the signals remain unexplained, presumably due to deficiency in the hydrologic model and errors in satellite perturbation models when the time-varying gravity field observables are computed from SLR data.

3.1.5.4. 18.6-year Tide

The largest impediment to extracting the secular signals in the orbital excitations is due to the 18.6-year zonal tide. While the Earth behaves almost elastically in the diurnal and semidiurnal tidal bands, its response at the much smaller frequency of the 18.6-year tide is significantly affected by anelasticity. Recently both the Starlette and Lageos-1 SLR target satellites passed their 19th year in orbit and this span of time is now adequate to separate the 18.6-year variation from the secular variation (see next section). Results were recently reported [Eanes and Bettadpur, 1995; Cheng et al., 1995] for the 18.6-year tide solution. Eanes and Bettadpur [1995] explain this signal in terms of perturbations to the shear modulus of the lower mantle at this frequency. Successful extraction and interpretation of this signal will allow more recently launched SLR targets, with shorter observation records, to be used for constraining the secular signal with greater accuracy than was possible before.