Gravity field estimation for next generation satellite missions
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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.