This study compares four approaches of local quasigeoid modelling using GNSS/levelling height anomalies. The first two approaches utilise only a dense network of points with known GNSS/levelling height anomalies and the EGM2008 model. They are based on the interpolation of residual values of height anomalies by applying the least squares collocation (LSC) and the thin plate spline (TPS). The next two approaches use additional data in the form of surface gravity data and the digital elevation model. One of these approaches is based on the classical Molodensky method combined with LSC. The other approach utilises the method of geophysical gravity data inversion (GGI). During the research, the authors used a local network of points with precisely defined GNSS/levelling height anomalies located in South-Western Poland. They obtained comparable results for all tested approaches at the maximum analysed density of GNSS/levelling points (about ). The differences between the modelling results became apparent only with an increase in the distance between the GNSS/levelling data points and the reduced accuracy of the used global geopotential model.

The analyses performed in this study relate to the method of quasigeoid modelling which uses the geophysical gravity data inversion technique (GGI method). The purpose of the analyses was to estimate the optimal values of quantitative parameters of selected input data used in the calculations. In particular, the following parameters were investigated: extents of a digital elevation model and the Moho depth model, the extent of the area covered by gravity data and density of gravity data. In order to perform the analyses, a series of local quasigeoid models was determined with different values of the above-mentioned parameters. The optimal values of the parameters were subsequently estimated based on the analyses of changes of quasigeoid models.

This paper presents the results of research and analyses related to the development of a new quasigeoid model fitted to GNSS/levelling data for the area of Poland (PL-geoid2021). The model was determined employing two procedures based on the Geophysical Gravity data Inversion technique (GGI method): procedure A consisted of the determination of the gravimetric quasigeoid model in the first step and its subsequent fitting to GNSS/levelling data in the second step, and procedure B consisted of a one-step determination of the model fitted to GNSS/levelling data. Both models were developed using the global geopotential model SGG-UGM-2 and gravity data covering the area of Poland, and slightly extend beyond Poland's southern and northern borders. The average model was adopted as the final model. It was demonstrated that the accuracy of the gravimetric quasigeoid model had a very low dependence on the reference topographic mass density model used. On the basis of this model, the GNSS/levelling datasets were also assessed and outliers were identified. The estimated accuracy of the gravimetric model, determined based on four GNSS/levelling datasets, was in the range of ± 1.2 to ± 1.7 cm, in terms of the standard deviation of the differences between the measured and model-determined height anomalies. Due to partial lack of gravity data just beyond the Polish border, the edge effect was also analysed. The accuracy of the final quasigeoid model (estimated in the same way as the gravimetric model) ranges from ± 1.0 to ± 1.2 cm. It should be noted, however, that this assessment is not fully independent because three of the four sets of GNSS/levelling points used for it, were also used to build the final model.

This article concerns the development of gravimetric quasigeoid and geoid models using the geophysical gravity data inversion technique (the GGI method). This research work was carried out on the basis of the data used in the Colorado geoid experiment, and the mean quasigeoid (${\zeta }_m$) and mean geoid ($N_m$) heights, determined by the approaches used in the Colorado geoid experiment, were used as a reference. Three versions of the quasigeoid GGI models depending on gravity data were analyzed: terrestrial-only, airborne-only, and combined (using airborne and terrestrial datasets). For the combined version, which was the most accurate, a model in the form of a $1^{\prime }\times 1^{\prime }$ grid was calculated in the same area as the models determined in the Colorado geoid experiment. For the same grid, the geoid–quasigeoid separation was determined, which was used to build the geoid model. The agreement (in terms of the standard deviation of the differences) of the determined models, with ${\zeta }_m$ and $N_m$ values for the GSVS17 profile points, was $\pm 0.9 \mathrm{c}\mathrm{m}$ for the quasigeoid and $\pm 1.2 \mathrm{c}\mathrm{m}$ for the geoid model. The analogous values, determined on the basis of all $1^{\prime }\times 1^{\prime }$ grid points, were $\pm 2.3 \mathrm{c}\mathrm{m}$ and $\pm 2.6 \mathrm{c}\mathrm{m}$ for the quasigeoid and geoid models, respectively.