The present study concerns the determination of ocean tide model parameters from GOCE orbital perturbation analysis. The GOCE satellite was
launched by the European Space Agency in 2009 and is flying on a Sun-synchronous near circular orbit, at the very low altitude of about 250 km which makes it very sensitive to tidally
induced orbit perturbations. The strategy adopted for analyzing GOCE GPS tracking data is the direct fully-dynamic approach, consisting in the
GOCE precise orbit determination (POD) and accumulation of the normal equations for each orbital arc, followed by a multiarc solution for the estimation of the global ocean tide parameters.
The GOCE GPS observations are processed using the NAPEOS S/W system (ESA/ESOC), specific for satellite orbit determination and prediction, upgraded to inclusion of the partial derivatives with respect to the ocean tide parameters and the ocean tide model inversion capability.
A sensitivity study of the ocean tide perturbations on GOCE orbit was carried out using as a reference the FES2004 model, in order to define the set of tidal harmonic parameters affecting GOCE orbit. In particular, the secular rates of the GOCE angular elements are estimated through a linear least-square fit.
From GOCE mean orbital characteristics, the spectral analysis of ocean tide perturbations in the radial, transverse and normal direction is performed using Kaula's linear satellite theory. Then, the perturbation statistics by coefficient is computed, obtaining a maximum RMS of about 1.323 m for the radial component, 363.136 m for the transverse component and 76.241 m for the normal component. The temporal aliasing problem is also accounted for the recovery of tidal parameters with GOCE and the principal alias periods are calculated for each tidal perturbation frequency, considering the length of the available GOCE data record. To fix a limit for the number of parameters to be estimated, three different cutoffs are applied to the RMS perturbation coefficients, respectively equal to 5 mm for the radial component, 2 cm for the transverse component and 1 cm for the normal component, both in the prograde and retrograde case. The total parameters to be estimated result to be 490.
GOCE data are processed to perform the fully-dynamic POD over daily orbital arcs from the 1st November 2009 until the 31st May 2011, but only arcs with a post-fit RMS of the GPS phase observations residuals lower than 8 mm are considered for the multiarc processing, for a total of 431 days.
The obtained preliminary results show the relative error of the estimated parameters with respect to the corresponding FES2004 parameters lower than 1 for about the 16\% of the total, meaning that they are of the order of magnitude of the FES2004 parameters.
GOCE orbital data were reprocessed along the same period of the previous run, initializing the ocean tide model with the estimated parameters, if present, and maintaining otherwise the FES2004 parameters. The post-fit RMS of the GPS phase residuals obtained with the new ocean tide model has a mean value of 6.5 mm, and it is noteworthy that the difference between the post-fit RMS obtained with the FES2004 model and that resulting from the new ocean tide model indicates a mean improvement of about 0.6 mm in for the 96\% of the analyzed arcs and greater than 1 mm for the 16\%, few days reach a difference of 2 mm.
Finally, the orbits obtained with the estimated parameters are compared with the orbits obtained employing the FES2004 model and the official GOCE Reduced-Dynamic PSO. The 3D RMS of the difference between the orbits computed using FES2004 and those recomputed with the new parameters shows a mean value of 2.5 cm, while the 3D RMS of the difference with respect to the official R/D PSO has a mean value of 4.9 cm. Moreover, the difference between the 3D RMS of the orbit residuals between the R/D PSO and the GOCE POD with FES2004 and the RMS of the difference between the GOCE R/D PSO and the GOCE POD with the new parameters results to have a mean improvement of 0.9 cm.
Further POD-Multiarc runs are certainly necessary, together with the refinement of the list of parameters to be estimated, removing excessively ill-estimated ocean tide parameters and introducing new parameters where appropriate.
Indeed, the model parameter tuning and investigation is essential to adjust the best combination of parameters to be estimated. Moreover, an extension of the data set to much longer time-period should allow a substantial improvement of the obtained results. The task has proven very intensive and challenging, but the partial results obtained are encouraging and a motivation for future analysis
