On the Definition and Realization of a Global Vertical Datum

AGlobal Vertical Datum (GVD) is naturally defined by the geoid, and there is a well-established consensus to adopt Gauss-Bessel-Listing's definition of the geoid (i.e. as being the level surface of the Earth's gravity field that best fits the undisturbed sea level). Themain problem in defining the geoid is therefore to fix its constant geopotential (W0). Nevertheless, this definition can be interpreted as to fit either the geopotential of sea surface to a constant (W0), or to minimize the height of sea level with respect to the geoid. Although the two interpretations lead to apparently different solutions, we show that they are practically the same. To improve the estimation ofW0 , we propose to weight the included data according to their a priori error estimates. Finally we discuss the use of GNSS/levelling data for vertical datum connections, concluding that such data, although indispensable for regional vertical datum connections, in combination with satellite altimetry over the oceans are practically useless for determining the GVD. Also, such a joint adjustment of the GVD and regional vertical datum biases yields inferior local connections vs. a separate adjustment with fixed GVD.