||Amplification of the Monthly Variation of the Oceanic Geoid from Self-Gravitation and Mass Conservation
Preliminary gravity results from GRACE up to harmonic degree ~10 show robust signatures of seasonal water concentrations in major continental drainage basins, consistent with the predictions from currently available hydrological models. In contrast, over the ocean the predicted geoid variability from available ocean general circulation models (OGCM) are, in general, systematically weaker than that of GRACE. This inconsistency in oceanic geoid variability may be due to problems with the GRACE data or the modeling. Normally, the oceanic geoid in GRACE is weaker than the hydrological geoid, as mass changes are much less localized over the ocean than over the land. Thus, the GRACE geoid over the ocean is more susceptible to observation errors than over the land. On theoretical grounds, a major problem in the predicted oceanic geoid signal is the lack of total mass conservation in the OGCM. In particular, mass exchange between hydrology and the ocean, which can amount to 2~3 cm of uniform sea level variations, is not accounted for by the OGCM. The non-uniform, realistic distribution of this exchanged mass can be important in the geoid variability over the ocean. In this paper, we develop the theory of a unified global geoid for the hydrological and the oceanic masses. The unified geoid is due to the self-gravitation of five distinct masses, two of which are the prescribed hydrology mass, and the volume-conserving mass anomaly integrated over the ocean depth, both taken from available models. The remaining masses are associated with the deformed elastic Earth, the volumetric change due to the deformed sea floor, and the surface distribution of exchanged mass (SDEM). The added SDEM conserves the total mass, and is determined based on the least potential energy principle. Semi-analytical solutions are developed in spherical harmonic expansions. Preliminary calculations up to harmonic degree 10 indeed show significant enhancement of the geoid signature over the ocean. Comparisons are made with monthly ocean surface salinity at the same harmonic truncation. Our results suggest that at least part of the lower degree GRACE geoid spectrum over the ocean corresponds to the signals associated with SDEM.