Impact of Scale Factor and Baseline Errors on Gravity Field Estimation: Analysis and Validation with GRACE Follow-On Data and Simulations

Gravity measurements from Low-Low Satellite-to-Satellite Tracking (LL-SST) systems, such as GRACE and GRACE-FO, collect gravity field data using GPS-observed orbits and variations in inter-satellite distances measured by inter-satellite ranging systems. Unlike GRACE, GRACE-FO uses a Laser Ranging Interferometer (LRI) designed as a technology demonstrator for future gravity missions. Some issues, such as an uncertainty in the absolute laser frequency causing an LRI scale factor error, and baseline errors in the GPS observations, i.e., offsets in the 200 km separation, can lead to significant effects on the gravity field. These effects were evaluated by developing an analytical relationship between the observations and the spherical harmonic coefficients (SHCs) of the gravity field. Both the LRI scale factor and baseline errors affect the SHCs in a comparable manner, leading to significant non-stochastic errors, especially at the low levels of the gravity field. Numerical simulations show that a scale factor of 1E-8 results in a geoid height error of about 0.074 mm at degree 2. This effect exceeds that of the atmospheric and ocean de-aliasing (AOD) model errors. Furthermore, a comparison of the LRI scale factor time series for data from GRACE-FO in 2021-2022, based on the theoretical form developed here, with a scale factor calculated by cross-calibrating KBR and LRI, showed a consistency between the two, with an estimated uncertainty of about 5.75E-8. The analytical formulation presented here effectively describes the influence of the scale factor or baseline error on LL-SST gravity missions.