Twelve years of developments: Geoidal geopotential $W_0$ for the establishment of a World Height System-present state and future

Abstract

Satellite altimetry missions, in particular the TOPEX/POSEIDON and Jason 1, have enabled a new realization of a World Height System. From altimetry data and precise global gravity models, one can determine a geopotential value $W_0$, which best fits the world’s oceans. $W_0$ specifies the geoid and it can also represent the WHS height datum. During the past 12 years, we have monitored the stability of the geopotential $W_0$ and proposed a rounded value of $W_0$ = 62 636 856.0 m2s-2 that reflects the formal and calibration uncertainties. However, for WHS, $W_0$ can be chosen arbitrarily. A methodology of connecting regional vertical datums and the proposed WHS has also been developed. The proposed approach, which requires vertical datums with sufficient numbers of GPS/levelling points, covering sufficiently large areas, has been successfully used to connect vertical datums in many parts of the world. The fundamental relativistic constant, required for relativistic time transformation, adopted by IAU, is based on our value of $W_0$. Since future precise clocks may be capable of “measuring” geopotential differences (heights) with respect to the fundamental relativistic constant (and $W_0$), it is essential that the future WHS, $W_0$ and the relativistic transformation are mutually consistent.