Tidal geopotential dependence on Earth ellipticity and seawater density and its detection with the GRACE Follow-On laser ranging interferometer

Ocean tides produce significant gravitational perturbations that affect near-Earth orbiting spacecraft.  The gravitational potential induced by tidal mass redistribution is routinely modelled for global gravity analysis and orbit determination, although generally by assuming a spherical Earth and a uniform seawater density.  The inadequacy of these simplifications is here addressed.  We have developed an accurate yet efficient algorithm to compute the ocean tidal geopotential, allowing for Earth’s elliptical shape and variable seawater density.  Using this new computation, we find that (1) the effect of ellipticity is several percent of the tide signal over mid to high latitude regions, which is comparable to elevation error in the state-of-the-art ocean tide models; (2) the effect of seawater density variations on the potential is as large as 2-3 cm in water-height equivalent, primarily in deep water where density increases 2-3% from compressibility.  Our analysis of new GRACE Follow-On (GRACE-FO) laser ranging interferometer measurements reveals evident errors when ellipticity and density variations are ignored.  When accounted for, the GRACE-FO residual tidal gravity perturbations are reduced by half, depending on the adopted tide model; only the remaining half likely represents actual model elevation error.  The use of a spherical surface and a uniform seawater density is no longer tenable given the precision of gravity measurements from GRACE and GRACE-FO satellites.