On the Formulation of Gravitational Potential Difference Between the GRACE Satellites Based on Energy Integral in Earth Fixed Frame

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Two methods for computing gravitational potential difference (GPD) between the GRACE satellites using orbit data have been formulated based on energy integral; one in geocentric inertial frame (GIF) and another in Earth fixed frame (EFF). Here we present a rigorous theoretical formulation in EFF with particular emphasis on necessary approximations, provide a computational approach to mitigate the approximations to negligible level, and verify our approach using simulations. We conclude that a term neglected or ignored in all former work without verification should be retained. In our simulations, 2 cycle per revolution (CPR) errors are present in the GPD computed using our formulation, and empirical removal of the 2 CPR and lower frequency errors can improve the precisions of Stokes coefficients (SCs) of degree 3 and above by 1–2 orders of magnitudes. This is despite of the fact that the result without removing these errors is already accurate enough. Furthermore, the relation between data
errors and their influences on GPD is analysed, and a formal examination is made on the possible precision that real GRACE data may attain. The result of removing 2 CPR errors may imply that, if not taken care of properly, the values of SCs computed by means of the energy integral method using real GRACE data may be seriously corrupted by aliasing errors from possibly very large 2 CPR errors based on two facts: (1) errors of ¯C2,0 manifest as 2 CPR errors in GPD and (2) errors of ¯C 2,0 in GRACE data—the differences between the CSR monthly values of ¯C 2,0 independently determined using GRACE and SLR are a reasonable measure of their magnitude—are very large. Our simulations show that, if 2 CPR errors in GPD vary from day to day as much as those corresponding to errors of ¯C2,0 from month to month, the aliasing errors of degree 15 and above SCs computed using a month’s GPD data may attain a level comparable to the magnitude of gravitational potential variation signal that GRACE was designed to recover. Consequently, we conclude that aliasing errors from 2 CPR errors in real GRACE data may be very large if not properly handled; and therefore, we propose an approach to reduce aliasing errors from 2 CPR and lower frequency errors for computing SCs above degree 2.