Global Gravity Field Recovery From Satellite To Satellite Tracking Data With The Acceleration Approach

Contents Abstract xi Samenvatting xv Curriculum vitae xix Acknowledgements xxii 1. Introduction 1 2. Gravity field modeling from SST data: an overview 9 3. Gravity field modeling from CHAMP data 53 4. Gravity field modeling from GRACE hl-SST data 81 5. Gravity field modeling from GRACE ll-SST data 91 6. Analysis of results obtained from the 3RC approach 133 7. Summary, conclusions and recommendations 203 Bibliography 209 A. Autocorrelation 223 B. Gaussian Filtering 225

This book provides a sound theoretical basis for the the different gravity field recovery methods and the numerics of satellite-to-satellite tracking data. It represents lectures given at the ‘Wilhelm and Else Heraeus Autumn School’ in Bad Honnef, Germany, October 4-9, 2015. The emphasis of the school was on providing a sound theoretical basis for the different gravity field recovery methods and the numerics of data analysis. The approaches covered here are the variational equations (classical approach), the acceleration approach and the energy balance approach, all of which are used for global gravity field recovery on the basis of satellite observations. The theory of parameter estimation in satellite gravimetry and concepts for orbit determination are also included. The book guides readers through a broad range of topics in satellite gravimetry, supplemented by the necessary theoretical background and numerical examples. While it provides a comprehensive overview for those readers who are already familiar with satellite gravity data processing, it also offers an essential reference guide for graduate and undergraduate students interested in this field.

The temporal gravity solutions estimated from NASA/DLR’s Gravity Recovery And Climate Experiment (GRACE) mission, and its successor, NASA/GFZ’s GRACE Follow-On (GRACE-FO), manifested as mass transports within the Earth system, have been used for a wide variety of Earth Science and climate change studies since 2002. However, there is an around one-year gap between the two satellite gravity missions (2017-2018). ESA’s fifth Earth Explorer Mission, the Swarm 3-satellite constellation, equipped with geodetic quality GNSS tracking system, was proposed to fill the gravimetry observation climate record data gap, at a moderate spatial resolution. Here, I applied a modified decorrelated acceleration approach to recover temporal gravity field using the 3-satellite Swarm constellation GPS tracking data. This approach is based on the simple linear relation between the second time derivative of the orbit and the gravitational acceleration. However, the time derivative could highly amplify the noise and make the noise correlated. In addtion, GPS positioning also involves correlation noise. Therefore, two linear transformations were introduced to decorrelate the observation noise. Next, two adjustment methods were studied to optimally combine the three gravity components, namely along-track, cross-track, and radial direction, along with introducing relative weights among orbital arcs for the final optimal gravity field estimation. The Swarm-only temporal gravity solutions have a good to excellent agreement with the overlapping GRACE/GRACE-FO solutions at least up to spherical harmonics degree around 13 (~1500 km, half-wavelength). Swarm-only temporal gravity solutions were then used to fill the mass change data gap over Greenland and West Antarctica ice-sheets during 2017-2018. Over Greenland, Swarm observed mass anomalies agreed well within the time epochs that overlaped with GRACE (correlation coefficient (CC) = 0.62), and GRACE-FO (CC=0.78). Within the data gap year, Swarm observed mass anomalies were relatively small suggesting that the Greenland mass loss slowed down, where the estimated short-term linear trend dropped from -54.3 ± 1.9 mm/yr (2013-2016 from GRACE) to -13.3 ± 7.5 mm/yr (2016-2018 from Swarm). In addition, as compared with the relatively quiet 2015-2017 at 13.5 ± 14.7 mm/yr, Swarm observed a fast ice mass loss episode at -89.2 ± 9.4 mm/yr during the gap year over West Antarctica, which agreed well with the estimate from GRACE and GRACE-FO without considering the gap at -92.8 ± 2.8 mm/yr during 2017-2019. This fast mass loss episode observed by Swarm also supports that the offset between GRACE and GRACE-FO time series is indeed due to mass loss but not a systematic bias. The official GRACE/GRACE-FO gravity products are derived from K-/Ka Band range (KBR) rate observations. Alternatively, the range acceleration observations could be used to estimate temporal gravity based on the so-called acceleration approach. In this study, by means of satellite orbit refinement, novel error mitigation schemes, and proper stochastic model estimation, the representation of range accelration was significantly improved in the acceleration equation (admittance spectrum dropped from up to 7 to around 1), and the in-situ line-of-sight gravity difference (LOSGD) was estimated with a high fidelity (CC = 0.96 with Level 2 data predicted LOSGD). For the first time, the improved acceleration approach was implemented for global temporal gravity recovery using GRACE and GRACE-FO observed range accelerations. The temporal gravity solutions recovered using this approach are, in general, in good agreement with the GRACE official Level 2 data products, based on the comparisons of the global mass variation trends, and basin-scale mass anomalies times series. Particularly, the gravity solution correlations between solutions in this study and other solutions are higher during the GRACE-FO time span. Despite the loss of an accelerometer onboard one of the GRACE-FO satellites, this closer comparison could be attributable to the improved range observation quality and the reduced noise level, which is clearly shown in the gravity inversion formal error. Because the high-low GPS tracking data were not used in this study, the low degree sectoral coefficients are believed to be slightly degraded compared to other solutions. The conventional GRACE/GRACE-FO temporal gravity solutions are at monthly sampling, which cannot easily be used to study sub-monthly mass transport events. However, the satellite ground track coverage varies from time to time. For the denser coverage time, a sub-monthly temporal resolution could be reached. A shorter solution data span, less than half of the nominal monthly data span, would enable observing signals which propagates quicker than a month. I employed the improved acceleration approach developed in this study to estimate solutions for every 13 days with one day sliding windows, which gives a daily sampling rate. The daily mass anomalies estimated from these solutions are shown to have a high correlation with the Morakot Typhoon (2009) induced precipitation evolutions (CC=0.87). It is shown that GRACE data is able to monitor the Morakot Typhoon induced massive rainfall during its landfall over Taiwan, which lasted only several days, though left a vast destruction on human lives and properties. In addition to the conventional spherical harmonic solutions, the GRACE/GRACE-FO Data Centers also deliver alternative data products called the “mascon solution”. Constraints are applied during the inversion so that it is free from the conventional GRACE post-processing. This advantage makes it a better candidate for coastal sediment deposition studies. Here, I used the University of Texas Center for Space Research (CSR) RL06 mascon data product to quantify the sediment deposition in the Bay of Bengal. By subtracting the Glacial Isostatic Adjustment (GIA) forward model predicted mass anomalies, ocean mass anomalies and the early Holocene Sediment Isostatic Adjustment (SIA) forward model predicted mass anomalies from the total mass change observed by GRACE (2002-2017), I obtained the mass anomalies estimation induced by the sediment discharge and transport in the Bay area. The corresponding sediment deposition rate estimate is 0.5± 0.2 Gt/yr, which is only half of the Brahmaputra river annual sediment discharge. This study also suggested the current SIA model tended to underestimate the SIA induced subsidence approximately by a factor of 2. In conclusion, the gravity solutions estimated from Swarm GPS tracking data using the modified decorrelation acceleration approach are capable to capture temporal gravity signals up to around degree 13. The Swarm-only solutions are shown to be able to fill the data gap between GRACE and GRACE-FO over West Antarctica and directly observe a fast mass loss episode. For GRACE and GRACE-FO, the improved acceleration approach has estimated the in-situ LOSGD with a high quality as indicated by the high correlation (CC=0.96) with L2 product predicted values and the monthly gravity solutions estimated from LOSGD have a good to excellent agreement with the official L2 products. The resulting GRACE daily sampled 13-day gravity solutions are capable to observe and quantify the evolution of an example abrupt weather episode, the landfall of the 2009 Morakot Typhoon over Taiwan. The demonstration of this novel monitoring of cyclone, for the first time, allows feasibility of using gravimetry data for possible disaster management.

Abstract: By the middle of this decade, measurements from the CHAMP (CHAllenging of Minisatellite Payload) and GRACE (Gravity Recovery And Climate Experiment) gravity mapping satellite missions are expected to provide a significant improvement in our knowledge of the Earth's mean gravity field and its temporal variation. For this research, new observation equations and efficient inversion method were developed and implemented for determination of the Earth2s global gravity field using satellite measurements. On the basis of the energy conservation principle, in situ (on-orbit) disturbing potential and potential difference observations were computed using data from accelerometer- and GPS receiver-equipped satellites, such as CHAMP and GRACE. The efficient iterative inversion method provided the exact estimates as well as an approximate, but very accurate error variance-covariance matrix of the least squares system for both satellite missions. The global disturbing potential observable computed using 16-days of CHAMP data was used to determine a gravity field solution (OSU02A), is commensurate in geoid accuracy to other gravity models and yields improvement in the polar region at wavelengths longer than 800 km. The annual variation of Earth's gravitational field was estimated and compared with other solutions from satellite laser ranging analysis. The annual geoid change of 1 mm would be expected mostly due to atmosphere, continental surface water, and ocean mass redistribution. The correlation between CHAMP and SLR solutions was 0.6 to approx 0.8 with 0.7 mm of RMS difference. Based on the monthly GRACE simulation, the geoid was obtained with an accuracy of a few cm and with a resolution (half wavelength) of 160 km. However, the geoid accuracy can become worse by a factor of 7 because of spatial aliasing. The approximate error covariance was found to be a very good accuracy measure of the estimated coefficients, geoid, and gravity anomaly. The resulting recovered temporal gravity fields have about 0.2 mm errors in terms of geoid height with a resolution of 670 km. It was quantified that how significant the effects due to the inherent modeling errors and temporal aliasing caused by ocean tides, atmosphere, and ground surface water mass are on monthly mean GRACE gravity estimates.

Significant advances in the scientific use of space based data were achieved in three joint interdisciplinary projects based on data of the satellite missions CHAMP, GRACE and GOCE within the R&D program GEOTECHNOLOGIEN. It was possible to explore and monitor changes related to the Earth’s surface, the boundary layer between atmosphere and solid earth, and the oceans and ice shields. This boundary layer is our habitat and therefore is in the focus of our interests. The Earth’s surface is subject to anthropogenetic changes, to changes driven by the Sun, Moon and planets, and by changes caused by processes in the Earth system. The state parameters and their changes are best monitored from space. The theme “Observation of the System Earth from Space” offers comprehensive insights into a broad range of research topics relevant to society including geodesy, oceanography, atmospheric science (from meteorology to climatology), hydrology and glaciology.

These proceedings contain 23 papers, which are the peer-reviewed versions of presentations made at the Joint Scientific Assembly of the International Association of Geodesy (IAG) and the International Association of Seismology and Physics of the Earth’s Interior (IASPEI). The assembly was held from 30 July to 4 August 2017 in Kobe, Japan. The scientific assembly included seven symposia organized by IAG, and nine joint symposia, along with additional symposia organized by IASPEI. The IAG symposia were structured according to the four IAG Commissions and the three GGOS Focus Areas, and included reference frames, static and time-variable gravity field, Earth rotation and geodynamics, multi-signal positioning, geodetic remote sensing, and GGOS. The joint symposia included monitoring of the cryosphere, studies of earthquakes, earthquake source processes, and other types of fault slip, geohazard warning systems, deformation of the lithosphere, and seafloor geodesy. Together, the IAG and joint symposia spanned a broad range of work in geodesy and its applications.

These proceedings include the written version of 130 papers presented at the International Association of Geodesy IAG2009 "Geodesy for Planet Earth" Scientific Assembly. It was held 31 August to 4 September 2009 in Buenos Aires, Argentina. The theme "Geodesy for Planet Earth" was selected to follow the International Year of Planet Earth 2007-2009 goals of utilizing the knowledge of the world’s geoscientists to improve society for current and future generations. The International Year started in January 2007 and ran thru 2009 which coincided with the IAG2009 Scientific Assembly, one of the largest and most significant meetings of the Geodesy community held every 4 years. The IAG2009 Scientific Assembly was organized into eight Sessions. Four of the Sessions of IAG2009 were based on the IAG Structure (i.e. one per Commission) and covered Reference Frames, Gravity Field, Earth Rotation and Geodynamics, and Positioning and Applications. Since IAG2009 was taking place in the great Argentine city of Buenos Aires, a Session was devoted to the Geodesy of Latin America. A Session dedicated to the IAG’s Global Geodetic Observing System (GGOS), the primary observing system focused on the multidisciplinary research being done in Geodesy that contributes to important societal issues such as monitoring global climate change and the environment. A Session on the IAG Services was also part of the Assembly detailing the important role they play in providing geodetic data, products, and analysis to the scientific community. A final Session devoted to the organizations ION, FIG, and ISPRS and their significant work in navigation and earth observation that complements the IAG.

This volume of proceedings is a collection of refereed papers resulting from the VI Hotine-Marussi Symposium on Theoretical and Computational Geodesy. The papers cover almost every topic of geodesy, including satellite gravity modeling, geodynamics, GPS data processing, statistical estimation and prediction theory, and geodetic inverse problem theory. In addition, particular attention is paid to topics of fundamental importance in the next one or two decades in Earth Science.