Regularization of the Gravity Field Inversion Process with High-Dimensional Vector Autoregressive Models

Earth's gravitational field provides invaluable insights into the changing nature of our planet. It reflects mass change caused by geophysical processes like continental hydrology, changes in the cryosphere or mass flux in the ocean. Satellite missions such as the NASA/DLR operated Gravity Recovery and Climate Experiment (GRACE), and its successor GRACE Follow-On (GRACE-FO) continuously monitor these temporal variations of the gravitational attraction. In contrast to other satellite remote sensing datasets, gravity field recovery is based on geophysical inversion which requires a global, homogeneous data coverage. GRACE and GRACE-FO typically reach this global coverage after about 30 days, so short-lived events such as floods, which occur on time frames from hours to weeks, require additional information to be properly resolved. In this contribution we treat Earth's gravitational field as a stationary random process and model its spatio-temporal correlations in the form of a vector autoregressive (VAR) model. The satellite measurements are combined with this prior information in a Kalman smoother framework to regularize the inversion process, which allows us to estimate daily, global gravity field snapshots. To derive the prior, we analyze geophysical model output which reflects the expected signal content and temporal evolution of the estimated gravity field solutions. The main challenges here are the high dimensionality of the process, with a state vector size in the order of 103 to 104, and the limited amount of model output from which to estimate such a high-dimensional VAR model. We introduce geophysically motivated constraints in the VAR model estimation process to ensure a positive-definite covariance function.