The Acceleration Approach

Abstract

The Gravity Recovery and Climate Experiment (GRACE) mission is a key instrument to monitor and understand variations in the mass distribution of the Earth. The primary observable is the (biased) range between the two satellites which is a geometric observation. The task is therefore to connect this kind of observation to the physically meaningful gravity field of the Earth or in other words connecting the kinematic observation to a force. Various approaches exist. Here, the focus is on the so-called acceleration approach which conceptually tries to avoid the solution of the variational equations by linking observed range accelerations to the gradient of the gravitational potential. Practically, it requires the observation of range accelerations, the attitude and their changes with matching precision in all three dimensions which are currently not available for GRACE. Three possible solutions are presented: (1) an approximate solution neglecting terms with low precision observations by reducing the basic equation to residual quantities, (2) a stringent solution by considering the term of low precision as unknown and solving it via the variational equations and (3) an alternative description using rotational quantities. Only the second approach yields solutions at the same level of precision as other approaches but offers no conceptual or computational advantage due to the need for solving the variational equations. The first kind of solution results primarily in a mis-modeling of long-wavelength signal but may still serve well for local or regional solutions. The third kind of solution is currently not feasible since the required precision in the attitude information is far from being available. However, it offers interesting insight into the observation system. It allows to describe GRACE as a two-dimensional observation system and explain mathematically the poor East-West sensitivity yielding the striping artifact in today’s GRACE solutions.