A least-squares collocation procedure to merge local geoids with the aid of satellite-only gravity models: the Italian/Swiss geoids case study

Abstract

Neighbouring countries often have national geoids that do not fit to each other, typically showing a discontinuity along the border. Among other effects, this discontinuity is mainly due to the different height datum, producing biased local geoids which can also have different accuracies and spatial resolutions. In some applications, for instance in case of international civil engineering works, a merging between two neighbouring geoids can be necessary. Obviously this procedure cannot be done by simply averaging overlapping areas completely disregarding biases. This paper deals with this problem in connection to the availability of data from satellite gravity missions. In contrast to terrestrial gravity anomalies, gravity and geoid models derived from satellite gravity missions, and in particular from GRACE and GOCE, do not suffer from those inconsistencies. These models in fact are not affected by local biases (local reference systems) since they do not make use of any ground gravity data or levelling. Basically this means that these models can provide the long wavelengths of the resulting merged geoid, in this way removing national biases or other systematic effects. On the other hand, the short wavelengths will directly come from a combination of the available local geoids. This article proposes a least-squares collocation procedure to merge local geoids with the help of these satellite-only gravity models. Even if the correct approach to produce a unique unbiased geoid is to start from the original terrestrial gravity data together with satellite data, the presented procedure can be helpful to merge already available local models. After a review of the mathematical formulation of the problem, the paper illustrates the case of the merging of the Italian and Swiss geoids, more specifically the Swiss CHGeo2004 and the Italian ITALGEO2005 pure gravimetric local models. A constant bias with respect to the GOCE reference (WGS84 ellipsoid) of about 100 cm for the Italian local geoid and of about 80 cm for the Swiss one have been estimated and removed. After that a unique geoid with an accuracy of few centimetres has been computed by collocation. A first application of this new geoid, named GISgeo2012 (GOCE, Italian and Swiss geoid) will be within the interreg project Helidem (HELvetia-Italy Digital Elevation Model) to create a new unified digital elevation model in orthometric height.