Tilo Reubelt

Comparing seven candidate mission configurations for temporal gravity field retrieval through full-scale numerical simulation

The goal of this contribution is to focus on improving the quality of gravity field models in the form of spherical harmonic representation via alternative configuration scenarios applied in future gravimetric satellite missions. We performed full-scale simulations of various mission scenarios within the frame work of the German joint research project “Concepts for future gravity field satellite missions” as part of the Geotechnologies Program, funded by the German Federal Ministry of Education and Research and the German Research Foundation. In contrast to most previous simulation studies including our own previous work, we extended the simulated time span from one to three consecutive months to improve the robustness of the assessed performance. New is that we performed simulations for seven dedicated satellite configurations in addition to the GRACE scenario, serving as a reference baseline. These scenarios include a “GRACE Follow-on” mission (with some modifications to the currently implemented GRACE-FO mission), and an in-line “Bender” mission, in addition to five mission scenarios that include additional cross-track and radial information. Our results clearly confirm the benefit of radial and cross-track measurement information compared to the GRACE along-track observable: the gravity fields recovered from the related alternative mission scenarios are superior in terms of error level and error isotropy. In fact, one of our main findings is that although the noise levels achievable with the particular configurations do vary between the simulated months, their order of performance remains the same. Our findings show also that the advanced pendulums provide the best performance of the investigated single formations, however an accuracy reduced by about 2–4 times in the important long-wavelength part of the spectrum (for spherical harmonic degrees

Comparison of GOCE-GPS gravity fields derived by different approaches

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Future Gravity Field Satellite Missions

<50), compared to the Bender mission, can be observed. Concerning state-of-the-art mission constraints, in particular the severe restriction of heterodyne lasers on maximum range-rates, only the moderate Pendulum and the Bender-mission are beneficial options, of course in addition to GRACE and GRACE-FO. Furthermore, a Bender-type constellation would result in the most accurate gravity field solution by a factor of about 12 at long wavelengths (up to degree/order 40) and by a factor of about 200 at short wavelengths (up to degree/order 120) compared to the present GRACE solution. Finally, we suggest the Pendulum and the Bender missions as candidate mission configurations depending on the available budget and technological progress.

GOCE Long-Wavelength Gravity Field Recovery from 1s-Sampled Kinematic Orbits Using the Acceleration Approach

The aim is to present and to examine an algorithm for the orbit analysis of a low-Earthorbiting GPS-tracked satellite to determine the spherical harmonic coefficients of the Earth’s gravitational field. By means of Newton’s interpolation scheme the accelerations acting on the satellite are derived from the satellite’s GPSpositions x(t k ), y(t k ), z(t k ) or position differences Δx,(t k-1 k ), Δy(t k-1 k ), Δz(t k-1 k ). This is done in a quasiInertial Reference Frame to avoid frame accelerations. The acceleration vector is balanced due to Newton’s equation of motion by the gravitational force vector, namely the gradient of the gravitational potential. The coordinates of the gradient of the gravitational potential, which are given in a Cartesian representation, also have to be transformed to the quasi-Inertial Reference Frame. The resulting equation system is then solved by means of a Gauss-Markov model. In order to get a more stable solution for higher resolutions a regularization method (Tikhonov, Kaula) can be applied.

Comparison of Kinematic Orbit Analysis Methods for Gravity Field Recovery

Several techniques have been proposed to exploit GNSS-derived kinematic orbit information for the determination of long-wavelength gravity field features. These methods include the (i) celestial mechanics approach, (ii) short-arc approach, (iii) point-wise acceleration approach, (iv) averaged acceleration approach, and (v) energy balance approach. Although there is a general consensus that—except for energy balance—these methods theoretically provide equivalent results, real data gravity field solutions from kinematic orbit analysis have never been evaluated against each other within a consistent data processing environment. This contribution strives to close this gap. Target consistency criteria for our study are the input data sets, period of investigation, spherical harmonic resolution, a priori gravity field information, etc. We compare GOCE gravity field estimates based on the aforementioned approaches as computed at the Graz University of Technology, the University of Bern, the University of Stuttgart/Austrian Academy of Sciences, and by RHEA Systems for the European Space Agency. The involved research groups complied with most of the consistency criterions. Deviations only occur where technical unfeasibility exists. Performance measures include formal errors, differences with respect to a state-of-the-art GRACE gravity field, (cumulative) geoid height differences, and SLR residuals from precise orbit determination of geodetic satellites. We found that for the approaches (i) to (iv), the cumulative geoid height differences at spherical harmonic degree 100 differ by only

Impact of Groundtrack Pattern of Double Pair Missions on the Gravity Recovery Quality: Lessons from the ESA SC4MGV Project

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