Estimation of the zero-height geopotential level W o LVD in a local vertical datum from inversion of co-located GPS, leveling and geoid heights: a case study in the Hellenic islands

Abstract

The estimation of the zero-height geopotential level of a local vertical datum (LVD) is a key task towards the connection of isolated physical height frames and their unification into a common vertical reference system. Such an estimate resolves, in principle, the 'ambiguity' of a traditional crust-fixed LVD by linking it with a particular equipotential surface of Earth's gravity field under the presence of an external geopotential model. The aim of this paper is to study the estimation scheme that can be followed for solving the aforementioned problem based on the joint inversion of co-located GPS and leveling heights in conjunction with a fixed Earth gravity field model. Several case studies with real data are also presented that provide, for the first time, precise estimates of the LVD offsets for a number of Hellenic islands across the Aegean and Ionian Sea.

High-frequency analysis of Earth gravity field models based on terrestrial gravity and GPS/levelling data: a case study in Greece

“…These values are valid for EGM2008 and EIGEN-6Cstat models up to their maximum degree. This small discrepancy in bias estimation is justified due to systematic differences in the Hellenic vertical datum among the mainland and islands (Kotsakis et al 2012. Our bias estimation is in close agreement with Tziavos et al (2012) who obtained a mean value of 75 cm for EGM2008 based on GPS/levelling data in the region of Thessaloniki in Northern Greece.…”

“…The orthometric heights of the national triangulation network's benchmarks were estimated through spirit and trigonometric leveling ties with the national leveling network. Numerical investigations on the assessment of the Hellenic vertical datum have been carried out by Kotsakis et al (2012), Grigoriadis et al (2014) for the case of the Hellenic islands and Andritsanos et al (2014), Tziavos et al (2012) for selected regions in Central and Northen Greece.…”

The GBVP approach for vertical datum unification: recent results in North America

“…It has been suggested to take these systematic levelling errors and distortions into account through a parametric model included in the observation equation. Kotsakis et al (2012) tested three different parametric models to remove the existing systematic errors and distortions in the estimation of the Greek islands (2013) have done numerical investigations on the use of the different parametric models for the estimation of the datum offsets in North America. It was shown that the 2-parameter model, which accounts for the north-south and east-west tilts of the LVD, is the best model as it resulted in the smallest RMS value of the geoid height differences.…”

“…A detailed review of the different systematic and random error sources in the estimation of vertical datum offsets is provided by Kotsakis et al (2012). In this section, we focus on the sensitivity of the estimated offsets and their accuracy to the errors of the available data sets used in Eq.…”

“…(5) needs to be taken into account in the accuracy analysis, as well. The uncertainty of the geocentric gravitational constant GM, i.e., σ GM , affects the accuracy of the estimated offset of the LVD with respect to the global geoid as follows (Kotsakis et al 2012):…”