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For the past, nearly 15 years, the Gravity Recovery and Climate Experiment (GRACE) has provided an invaluable view of mass variability in the Earth system. During its time on orbit it has enabled unprecedented contributions to hydrology, oceanography, and the cryosphere; however, GRACE is currently approaching the end of its lifetime. As this approaches and future dedicated satellite gravity missions are poised to continue its legacy, it's important to highlight limitations in our current knowledge and explore areas of improvement for future analysis. This work returns to the first principles of gravity field estimation and explores some of the basic assumptions and idiosyncrasies inherent in the estimation of Earth's gravitational field. Current gravity field estimation from GRACE attempts to optimally combine GPS observables, which provide absolute positioning, with high accuracy, relative inter-satellite measurements (KBR). While an optimal data fusion procedure is utilized, empirical analysis has indicated that artificial down-weighting of the GPS observable provides significant improvements to estimates of the gravitational field. The necessity of this ad-hoc treatment signals a misunderstanding in the contribution of each observable to gravity field estimates and deficiencies in the modeling of each observable. The analysis of this misunderstanding begins with an examination of the GPS observable's ability to independently recover estimates of the spherical harmonic coefficients. This not only provides insight into the effect of GPS on the gravitational field, but examines the efficacy of using a single satellite to fill a possible gap between GRACE and its follow-on mission. While these single satellite derived gravitational fields have limited accuracy, their combination with satellite laser ranging (SLR) allows for the determination of large spatial scale, long term trends from low degree harmonics (7x7). Additionally, thorough examination of the combined gravity field solutions indicates that the GPS observable is vital to stabilization of estimated parameters which perturb at low frequencies, a significant weakness for the relative inter-satellite ranging observable. These low frequency parameters -- which include the satellite initial conditions, accelerometer dynamicals, low degree harmonics, sectorial harmonics, and harmonics of resonant order -- are also the most susceptible to contamination by dynamical modeling error. Therefore, it is necessary to stochastically model the observation error with high fidelity, most notably the frequency dependence caused by errors in the background dynamical models. Accurate stochastic modeling of the observables is achieved by reexamining the GRACE estimation problem from the Bayesian perspective. This viewpoint highlights typical assumptions made in nominal GRACE processing, most importantly that observation errors are independently Gaussian distributed. Analysis of this assumption indicates its inaccuracy, necessitating the utilization of algorithms which enable modeling of the frequency dependence of the observable errors, through the observation covariance. The most important of these error sources is the manifestation of dynamical modeling error, which perturbs predominantly at low frequency and the orbital period, similarly to the main contributions of the GPS observable. Accounting for the frequency dependence of the observation errors shows the ability to improve optimal data fusion, reduce error in estimates of the gravitational field by mitigating stripes and, most importantly, drastically improves the formal characterization of error in the estimated gravitational fields; facilitating scientific interpretation and prognostication of Earth's climate variability, optimal combination with independent datasets and a priori constraints, and optimal assimilation of GRACE data products with Earth system models.
Modelling the gravity field of the Earth is important for many scientific disciplines. Global gravity models allow for the investigation of long-wavelength properties of the gravity field. Global models derived from satellite observations provide an additional benefit: they are uncorrelated with any error contaminating regional terrestrial gravity information; this makes them ideal for combination with terrestrial gravity data in order to formulate high-precision regional geoid models. This dissertation investigates several possible areas of improvement to both the formulation and evaluation of satellite-only global gravity models. The first major barrier is due to what is known to the geodetic community as the “polar-gap problem”: the lack of data collected by the satellites over the poles due to the inclination angle of their orbit. The second is the rigorous application of these models inside of the topographical masses (and most pertinent, on the surface of the geoid). These problems are addressed in three articles. The first presents a mathematical tool that can be used in order to address the polar-gap problem by performing the global integration making use of the additivity property of Riemann integrals. The second article presents a computational scheme that allows for the evaluation of various quantities derived from global gravity models inside the topographical masses. Finally, the third article describes the production and validation of a 2D global topographical density model that is required for the rigorous evaluation of the gravity field as prescribed in the second article.
Volume resulting from an ISSI Workshop, 11-15 March 2002, Bern, Switzerland