Gravity field models derived from the second degree radial derivatives of the GOCE mission: a case study

Abstract

<p class="Default">The GOCE satellite mission is one of the main achievements of the satellite geodesy for the Earth’s gravitational field recovery. Three different approaches have been developed for the estimation of harmonic coefficients from gradiometry data measured on board of GOCE-satellite. In this paper a special version of the space-wise method based on the second method of Neumann for fast determination of the harmonic coefficients <em>C<sub>nm</sub>, S<sub>nm</sub></em> of the Earth’s gravitational potential is given based on the radial gravity gradients of the EGG_TRF_2 product, except of two polar gaps filled by radial gradients from the EGM2008 gravity model. In the pre-processing stage GOCE-based second degree radial derivatives were averaged to the regular grid through Kalman static filter with additional Gaussean smoothing of residual radial derivatives. All computations are made by iterations. As the first step the determination of the preliminary NULP-01S<strong> </strong>model up to degree/order 220 derived from the Gaussean grid of the GOCE radial derivatives with respect to the WGS-84 reference field was developed based only one of the radial gradients EGG_TRF_2 in the EFRF-frame. In the second iteration the same algorithm is applied to build the NULP-02S gravity field model up to degree/order 250 using the same Gaussean grid with respect to the NULP-01S reference field. The NULP-02S model was verified by means of applying various approaches for the construction of the gridded gravity anomalies and geoid heights in the Black sea area using processing of datasets from six altimetry satellite missions. Comparison of different models with GNSS-levelling data in the USA area demonstrates the independent verification of achieved accuracy of the constructed NULP-02S Earth’s gravity field model.</p>

Geodynamics

“…On the contrary, we get large differences between (Cheng, et al, 2013;Marchenko et. al., 2018) results and this Solution I during the timeintervals (1976-2011) and (1976-2020) This leads to the idea to use the linear splines for better modeling of time-dependent parameters using suitable short intervals because the direct determination of ) (t H D from observation is not found in the literature sources.…”

“…Rubincam, 1984;Cheng et al, 1989;Schwintzer et al, 1991;Cheng et al, 2004;IERS Standards, 2010;Cheng et al, 2011;etc. Contrary to the linear model Cheng et al, 2013 applied the enhanced approximation with the quadratic term additionally to the linear model for the ) ( 20 t C time-series, during the time-interval from 1976 to 2011. Marchenko and Lopushansky (2018) used a similar approach for the period from 1976 to 2017 yr. and subinterval from 1992 to 2017 yr. It allowed revealing the long-term variations in 2 () According to Cheng et al, 2013 the linear model can be used successfully only on short time intervals.…”

“…There are different models chosen for time-dependent change of the coefficient 20 A (for example, Cheng et al, 2011;Cheng et al, 2013;etc). Here one starts from the 20 A model taken from the paper (Marchenko and Lopushansky, 2018) and representing the change in time as the long-term variation fixed at epoch J2000 was modeled by polynomials up to 2nd degree (blue line) simultaneously with Fourier series using annual period (red line) (solution II in Table 1).…”

“…The linear model is shown in green (solution III in Table 1) (Marchenko et. al., 2018) during the time-interval 1992-2020.…”