On reduction of the filtered GOCE SGG data from the orbit level to a mean orbit

The overall goal of the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, is to employ GOCE data products, mainly the original Satellite Gravity Gradiometry (SGG) data, and model the geoid in the Hellenic area and the surrounding regions. However, to utilize the original GOCE SGG data for geoid modeling, filtering is needed as well as a reduction to a mean orbit (MO) so that downward continuation to the Earth’s surface (ES) can be realized. After investigating various filtering options (Finite Impulse Response - FIR, Infinite Impulse Response - IIR, and wavelet multi-resolution analysis - MRA), both in the frequency and the space domain, it was concluded that an FIR with order 1500 would be the optimal one. This was based on both comparisons with upward continued gradients from the XGM2019 global geopotential model (GGM) and the spectrum cut-off of the various filters tested within the GOCE measuring bandwidth. Then, downward continuation of the filtered data to a mean sphere (MS) was necessary. With a maximum altitude, within the GOCE 3-year mission, close to 295 km and a minimum of about 240km, GOCE data generated at a mean level of 230 km. Regular 5’x5’ grids of the disturbing potential gradients Tij were generated using both XGM2190 and EGM2008 up to their maximum degree and order, while a combined solution using TIM-R6 to degree and order 165 and EGM2008 as fill-in was also used. The GGM information was used to simulate the downward continuation of Tij, so that this can then be applied to the actual GOCE data. The reduction to a MS was performed by estimating GGM gradient grids per 1 km from the MS to the maximum orbital level, and then using a linear interpolation for the reduction from the actual satellite height. It was found that the reduction with height of the gravity gradients varies linearly, while the use of XGM2019 provided the overall best results. After interpolating from the GGM grids, Tij values from XGM were estimated at the initial GOCE points and then used to reduce the GOCE SGGs to the MO. Finally, and in order to estimate residual Tij at the MO, three different options were tested. First, an analytical spherical harmonic synthesis (SHS) of and  at 230km was carried out. Then, the same effects were estimated using a grid of 1’x1’ disturbing potential gradients as well as a 5’x5’ grid. For each of these cases, the rigorous SHS and the two based on interpolation have been determined, showing that even a global 5’x5’ grid of disturbing potential gradients is sufficient and analytical determination of the GGM contribution is not necessary.