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Next-Generation Satellite Gravimetry for Measuring Mass Transport in the Earth System

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Next-Generation Satellite Gravimetry for Measuring Mass Transport in the Earth System Next-generation satellite gravimetry for measuring mass transport in the Earth system Proefschrift ter verkrijging van de graad van doctor aan de Technische Universtiteit Delft, op gezag van de Rector Magnificus Prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op 3 December 2015 om 12:30 uur door João Gregório DE TEIXEIRA DA ENCARNAÇÃO Master of Science in Aerospace Engineering, Delft University of Technology geboren te Funchal, Madeira, Portugal This dissertation has been approved by the: promotor: Prof. Dr.-Ing. habil. R. Klees copromotor: Dr. P.G. Ditmar Composition of the doctoral committee: Rector Magnificus, chairman Prof. Dr.-Ing. habil. R. Klees, Delft University of Technology Dr. ir. P.G. Ditmar, Delft University of Technology Independent members: Prof. dr. L.L.A. Vermeersen, Delft University of Technology Prof. dr. B. D. Tapley, Center for Space Research Prof. dr. A. Jäggi, Astronomical Institute of the University of Bern Prof. dr. F. Flechtner, GFZ German Research Centre for Geosciences Prof. dr. ir. R. Hanssen, Delft University of Technology, reserve member Other member: Dr. B. Gunter, Georgia Institute of Technology © 2015, João Gregório de Teixeira da Encarnação All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without prior permission from the copyright owner. ISBN 978-94-6259-953-6 Keywords: Earth Observation, Satellite Geodesy, Time-varying Gravity Field, Mass Transport Processes, GRACE follow-on Typeset by the author with the LATEXdocumentation system. The electronic version of this document contains hyperlinks between the references of citations, tables, figures, equations, sections and the corresponding definitions. In the bibliography, all Digital Object Identifier (DOI, www.doi.org) numbers are hyperlinks to the web page of the corresponding abstracts. All Uniform Resource Locators (URLs) are hyperlinks to the corresponding web page. All aforementioned hyperlinks are clickable but otherwise unmarked. Printed by Ipskamp Drukkers. To my ancestors. Contents Summary vii Samenvatting xi Acknowledgements xv 1 Introduction1 1.1 Background........................................1 1.1.1 A dynamic Earth...............................3 1.1.2 Observing a planet..............................4 1.2 Motivation.........................................5 1.2.1 Limitations of GRACE...........................6 1.2.2 Limitations of future gravimetric mission proposals.......9 1.3 Objectives and methods............................... 12 1.4 Outline........................................... 13 2 Satellite gravimetry for monitoring mass transport in the Earth system 15 2.1 Temporal aliasing in measuring mass transport processes........ 15 2.1.1 Spatio-temporal resolution........................ 16 2.1.2 Mitigating temporal aliasing....................... 17 2.2 Measuring Earth’s gravitational field from satellites............ 18 2.2.1 high-low Satellite-to-Satellite Tracking................ 19 2.2.2 Satellite gradiometry............................ 21 2.2.3 low-low Satellite-to-Satellite Tracking................. 23 i Contents 2.3 The GRACE mission.................................. 26 2.3.1 Contribution of GRACE to the advances in modelling the time-variable gravitational field..................... 26 2.4 Orbit accuracy of LEO satellites.......................... 31 2.4.1 Orbit determination methods...................... 31 2.4.2 Absolute LEO orbit positioning accuracy.............. 33 2.4.3 Relative LEO orbit positioning accuracy............... 37 2.5 Processing strategies.................................. 38 2.5.1 Variational equations approach..................... 38 2.5.2 Energy balance approach......................... 39 2.5.3 Boundary value problem for short arcs................ 40 2.5.4 Acceleration approach........................... 41 2.5.5 Classification.................................. 42 2.5.6 Correlated noise in gravimetric data.................. 42 2.6 Future gravimetric missions............................. 44 2.7 Summary.......................................... 48 3 Satellite formations for gravity field recovery 51 3.1 Orbital elements..................................... 52 3.2 Orbit stability...................................... 52 3.3 The trailing formation................................. 53 3.4 The pendulum formation............................... 55 3.4.1 The pendulum formation with along-track displacement.... 57 3.5 The cartwheel formation............................... 60 3.6 Relative orbital elements............................... 64 3.7 Distinction between similar formations..................... 64 3.7.1 Distinction between the pendulum and all other formations. 65 3.7.2 Distinction between trailing and cartwheel formations..... 65 3.8 Orbit simulation of Satellite Formations.................... 65 3.8.1 The Hill equations.............................. 66 3.8.2 The formation parameters......................... 68 3.8.3 Formations in elliptical mean orbits.................. 69 3.8.4 Inverse linear mapping........................... 70 3.8.5 Orbits of satellites formations under an aspherical gravita- tional field................................... 71 3.9 Summary.......................................... 74 ii Contents 4 Modelling Satellite Gravimetry 75 4.1 Functional Model.................................... 76 4.1.1 Processing of hl-SST observations................... 77 4.1.2 Processing of ll-SST observations................... 81 4.2 Signal Model....................................... 86 4.2.1 The “true” and reference force models................ 86 4.2.2 Static gravity field models........................ 87 4.2.3 The Atmosphere and Ocean De-aliasing Level 1B product.. 88 4.2.4 The Delft Mass Transport model.................... 89 4.3 Noise Model....................................... 89 4.3.1 Model errors.................................. 91 4.3.2 Modelling hl-SST noise.......................... 97 4.3.3 Modelling ll-SST noise........................... 98 4.3.4 Summary of the Noise types....................... 108 4.4 Summary.......................................... 109 5 Added Value of non-Dedicated GPS-Equipped Constellations 111 5.1 Introduction........................................ 111 5.2 Methodology....................................... 114 5.2.1 Simulation Setup............................... 118 5.3 Simulation Results................................... 122 5.4 Conclusions........................................ 126 6 Lessons learned from GRACE 129 6.1 Relative orbit accuracy of GRACE........................ 129 6.1.1 Considered orbits............................... 131 6.1.2 Analysis set-up................................ 132 6.1.3 Data screening................................ 133 6.1.4 Monthly RMS residuals.......................... 134 6.1.5 Total RMS residuals............................. 136 6.1.6 Spectra..................................... 137 6.1.7 Future relative position and velocity accuracy........... 140 6.2 Knowledge gained from GRACE data...................... 142 6.2.1 Production of noise realisations in GRACE data......... 142 6.2.2 Sources of noise in GRACE data.................... 146 6.2.3 Discussion and conclusions........................ 164 6.3 Validation and fine-tuning of the advanced noise model......... 166 6.3.1 Accelerometer noise............................. 169 6.3.2 Ranging noise................................. 171 iii Contents 6.3.3 Correction noise................................ 173 6.3.4 Orientation noise............................... 175 6.3.5 Positioning noise............................... 177 6.3.6 Summary.................................... 182 6.4 Conclusions........................................ 184 7 Positioning noise 187 7.1 Formation scenarios.................................. 187 7.2 Orbit simulation..................................... 189 7.2.1 Keplerian reference orbits......................... 189 7.2.2 Modelled orbits................................ 189 7.3 Orbital noise....................................... 191 7.3.1 Calibration of the positioning noise.................. 195 7.4 Analytical derivation of the components of the positioning noise... 197 7.4.1 Relative positioning noise......................... 197 7.4.2 Absolute positioning noise........................ 198 7.4.3 Positioning noise magnitudes...................... 199 7.5 Simulation of relative and absolute positioning noise............ 201 7.6 Conclusions........................................ 207 8 Satellite Formations 209 8.1 Simulation set-up.................................... 211 8.1.1 Formation scenarios............................. 212 8.1.2 Force model.................................. 213 8.1.3 Orbit simulation............................... 215 8.1.4 Data simulation................................ 215 8.1.5 Data inversion................................. 221 8.2 Results........................................... 221 8.2.1 Noise types................................... 222 8.2.2 Noise budgets................................. 234 8.2.3 Effect of the maximum range...................... 243 8.2.4 Spatial error patterns............................ 248 8.3 Technical aspects of future gravimetric missions............... 254 8.4 Summary and conclusions.............................. 255 9 Conclusion and recommendations 259 9.1 Summary.......................................... 260 9.2 Conclusions.......................................
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