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.

For the first time, we present a complete, processed compilation of all repeated absolute gravity (AG) observations in the Fennoscandian postglacial land uplift area and assess their ability to accurately describe the secular gravity change, induced by glacial isostatic adjustment (GIA). The data set spans over more than three decades and consists of 688 separate observations at 59 stations. Ten different organizations have contributed with measurements using 14 different instruments. The work was coordinated by the Nordic Geodetic Commission (NKG). Representatives from each country collected and processed data from their country, respectively, and all data were then merged to one data set. Instrumental biases are considered and presented in terms of results from international comparisons of absolute gravimeters. From this data set, gravity rates of change (⁠g˙⁠) are estimated for all stations with more than two observations and a timespan larger than 2 yr. The observed rates are compared to predicted rates from a global GIA model as well as the state of the art semi-empirical land uplift model for Fennoscandia, NKG2016LU. Linear relations between observed g˙ and the land uplift, h˙ (NKG2016LU) are estimated from the AG observations by means of weighted least squares adjustment as well as weighted orthogonal distance regression. The empirical relations are not significantly different from the modelled, geophysical relation g˙=0.03−0.163(±0.016)h˙⁠. We also present a g˙-model for the whole Fennoscandian land uplift region. At many stations, the observational estimates of g˙ still suffer from few observations and/or unmodelled environmental effects (e.g. local hydrology). We therefore argue that, at present, the best predictions of GIA-induced gravity rate of change in Fennoscandia are achieved by means of the NKG2016LU land uplift model, together with the geophysical relation between g˙ and h˙⁠.

Based on geostatistical modelling the authors compared relative sea level records for the Litorina and post-Litorina Sea with tide gauge and GPS derived crustal velocity measurements in Fennoscandia and in the Baltic region. Results show good fit between the geological record and GPS derived crustal velocity measurements indicating that the postglacial rebound (PGR) centre on the northwest coast of the Bothnian Sea and the isostatic zero-line in the southern Baltic remained stable during the last 8000 14C yrs BP (8900 cal yrs BP). An average Baltic Sea level rise of 1.4±0.4 mm/y for the 20th century was estimated, which is found to be at about one fifth compared to the mid-Holocene sea level rise. However, considering the recent estimates of eustatic sea level rise for the 21st century the slowly uplifting coastal areas in southern Sweden, SE Finland, Estonia, Latvia and NW Russia, which have experienced a long term relative sea level fall, will probably also be affected by future sea level rise reminiscent of the mid-Holocene one.

The deduction of a regularly spaced gravity anomaly grid from scattered survey data is studied, addressing mainly two aspects: reduction of gravity to anomalies and subsequent interpolation by various methods. The problem is illustrated in a heterogeneous study area and contrasting test areas including mountains, low terrains, and a marine area. Provided with realistic error estimates, Least Squares Collocation interpolation of Residual Terrain Model anomalies yields the highest quality gravity grid. In most cases, the Bouguer reduction and other interpolation methods tested are equally viable. However, spline-based interpolation should be avoided in marine areas with trackwise survey data.