The 5 mm geoid model for Estonia computed by the least squares modified Stokes’s formula

Abstract

Computational stages of a new high-resolution 5 mm quasigeoid model for Estonia are explained. Certain requirements for the quality and coverage of gravity data in the context of 5 mm geoid modelling were fulfilled. The present gravity data coverage over the target area is 1 point per 10 km2, less dense in adjacent land and marine areas. The average uncertainty estimate of gravity data within the target area is about 0.5 … 0.75 mGal. The gravity data were merged, cleaned, analysed, reduced and gridded to yield a seamless gravity anomaly field. A least squares modified Stokes formula (Sjöberg, L.E., 1991. Refined Least Squares Modification of Stokes Formula”. Manuscripta Geodaetica, 16, 367–375.) that combines local terrestrial gravity anomalies and the global geopotential model derived long-wavelength component in a truncated Stokes’s integral yielded the best gravimetric geoid modelling results. The combined uncertainty for most of the Estonian GNSS-levelling points is not exceeding 5 mm, allowing an adequate verification of the geoid modelling quality. Inter-comparison of the geoid model, GNSS-derived and spirit-levelled heights at discrete points was conducted for geoid modelling assessment. A two stage stochastic spatial prediction was applied to obtain an optimal fit between precise GNSS-levelling data and the geoid model. The location-specific post-fitting uncertainties of the resulting model EST-GEOID2017 revealed standard deviation of 4.2 mm, i.e. the same level as the accuracy of the used GNSS-levelling control points.