A simulation study for future satellite gravimetry missions

P. Miragaia Gomes Inacio

Research output: ThesisDissertation (TU Delft)

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The Gravity Recovery and Climate Experiment (GRACE), launched in 2002, was the first low-low satellite-to-satellite tracking (ll-SST) satellite gravity mission. One of its primary objectives was to monitor the redistribution of mass in the Earth's system, which is of vital importance not only to the scientific community, but also to society in general. GRACE allowed for the mass redistribution monitoring at much smaller spatial scales than ever before. The data collected by the mission lead to a proliferation of researches in many scientific domains. The GRACE mission, completed in 2017, was considered as an outstanding success. Consequently, the GRACE Follow-On (GFO) mission was launched in 2018 to continue its legacy. With the GFO mission underway, it is now timely to look into the future of satellite gravimetry. The major goal of this thesis was to design and benchmark a set of ll-SST mission concepts with the potential to deliver unprecedented accuracy of mass redistribution estimates. The approach taken was to develop a simulation tool capable of handling arbitrarily complex satellite mission designs. In the first instance, this tool was used to analyze the error budget of the GRACE mission. A combination of simulated errors from various sources showed a very good agreement with observed noise in the GRACE inter-satellite acceleration data. Noise in the frequency range between 1 and 9 mHz, the origin of which was previously unknown, was explained by a combination of positioning, acceleration and ranging errors and errors in the atmosphere and ocean de-aliasing model. A good agreement between simulated and actually observed noise was only possible by properly accounting for the propagation of errors through the computed reference orbits. I called this error propagation mechanism the indirect effect. I formally defined the indirect effect and demonstrated that it propagates differently in different types of ll-SST missions. Next, the error budget of future missions which replicate GRACE was simulated. I confirmed that temporal aliasing errors are the ones that limit the performance of these missions. A better instrumentation will not improve the performance of those missions in any significant way. New mission concepts are required in order to surpass the performance level of the current ones. Afterwards the tool was used to run small-scale simulations in order to gain insight into the mission design aspects which determine the performance of the mission. Small-scale simulations consider relatively short timespans (between 2 and 5 days) and the obtained solutions are typically computed up to a relatively low maximum SH degree (normally between 40 and 60). Using small-scale simulations, I could identify mission design aspects which impact the temporal and spatial resolution of ll-SST missions. Considering different gravity gradient directions as observables, I have shown that collecting multiple observables from a single formation greatly increases the spatial resolution of the mission compared to the single-observable case. This discovery begs the consideration of formations consisting of more than two satellites in order to maximize the spatial resolution. I have also considered missions consisting of multiple formations. For these, I have shown that temporal aliasing errors can be minimized by orienting the polar orbital planes of the satellite formations such that they equipartition 3-D space. Specifically, for two-formation missions, the orbital planes should be perpendicular, while for three-formation missions they should be set 60° apart. On the basis of the small-scale simulations, I have proposed a set of satellite missions, which were benchmarked with full-scale simulations. The missions were designed to combine multiple observables in a single or multiple formations. In the latter case, their orbital planes were correctly oriented in order to minimize temporal aliasing errors. Of the proposed concepts, missions which considered along-track/pendulum (which I called gamma) and along-track/cartwheel (which I called sigma) combinations were found to yield the lowest total errors. Of those, I selected the single-formation along-track/pendulum combination (gamma) mission as the most promising for future ll-SST mission. I have shown that this concept yields large improvements in terms of spatial and temporal resolutions. At the same time, the gamma mission avoids the complexities of the cartwheel pair of satellites and, given that it considers a single satellite formation, it is potentially cheaper and less complex than the other alternatives which considered two. The gamma mission shows substantially lower errors compared to existing ll-SST missions, which may be further reduced when used as the basis for a multi-formation constellation of satellites.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Delft University of Technology
  • Klees, R., Supervisor
  • Ditmar, P.G., Advisor
Thesis sponsors
Award date10 Sept 2020
Print ISBNs978-94-6366-311-3
Publication statusPublished - 10 Sept 2020


  • Temporal aliasing errors
  • Satellite formations
  • Satellite geodesy
  • Future gravity missions


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