## 4 Research Results  
### Assessment of the Accuracy of the Gravity Values and height Anomalies Determined from the GGI Model  
The accuracy analyses that we carried out examined four factors, as follows: DEM resolution, constant density zones dimensions, density of gravity data, and the initial density of topographic masses. The results of the analyses are presented in two parts, which will be described in following sections. Section 4.1.1 covers the first two factors and Section 4.1.2. covers the other two. This Section also includes a comparison with classical methods of gravity prediction. 1.1 The Impact of DEM Resolution and Constant Density Zones Dimensions on Determined Gravity Values and Height Anomalies  
In order to assess the significance of DEM resolution for the accuracy of the GGI model, the calculations were done using the four resolutions listed in Section 3. Each of the volumes \(\Omega\) and \(\kappa\) were divided into 3600 constant density zones with dimensions of about \(4\times 4\) km (7200 estimated constant densities). Calculations were performed assuming \(\rho_{0}=2670\) kg/m\({}^{3}\) as the reference density model for the volume \(\Omega\). The disturbing potential model was built based on the known points and according to the procedure described in Section 2.1. Due to the adoption of various datasets for the Polish and Slovak parts, the accuracy parameters were determined separately for the areas of both countries. For evaluating the gravity prediction, the test points were also separated in terms of their heights, giving the dependence of the accuracy of the model on this parameter. In respect to this, three groups of points were separated. The first group (\(H_{I}\)) represents points located in lowland terrain up to 300 m high, the second group (\(H_{II}\)) represents points located in the area of low mountains with heights between 300 m and 700 m, and the third group (\(H_{III}\)) has points located in the area of higher mountains with a height above 700 m. Differences \(\Delta\zeta=\zeta-\zeta_{GGI}\) and \(\Delta\mathrm{g}=\mathrm{g}-\mathrm{g}_{GGI}\) were determined for test points, where \(\zeta\) is the height anomaly determined from the adopted quasigeoid model, \(\mathrm{g}\) is the measured gravity, \(\zeta_{GGI}\) and \(\mathrm{g}_{GGI}\) are height anomaly and gravity calculated from the GGI model according to Equations (7) and (9) respectively, wherein the disturbing potential is calculated by Equations ((4), (5), (6) and (21)), and the gravity disturbance value is determined by Equation (8). Since the average values of the analyzed differences were close to zero, the standard deviations of these differences turned out to be almost the same as their RMS errors. Thus, Tables 1 and 2 show the standard deviations of these differences as indicators of the GGI model fit to the appropriate quasigeoid models and to the measured gravity. The tables also show the mean heights of the test points and the corresponding accuracy parameters of the EGM2008 model [29], accepting \(\Delta\zeta=\zeta-\zeta_{EGM08}\) and \(\Delta\mathrm{g}=\mathrm{g}-\mathrm{g}_{EGM08}\). Commenting on the above results, we should first point out the lack of dependence between the DEM resolution and the accuracy of the GGI model in terms of the disturbing potential (quasigeoid accuracy). Standard deviations of differences \(\Delta\zeta\) are at a similar level for all analyzed DEM resolutions. Looking at gravity disturbances, the results are slightly different. There is a clear relation between the used DEM resolution and the height of the test points and the accuracy of the model--which is as expected. Ultimately, it can be estimated that the average accuracy of the gravity disturbances (and thus gravity) determined from the GGI model for the best versions is about 1 mGal. There are also noticeable differences in standard deviations of \(\Delta\zeta\) for the Polish and Slovak parts. The designated GGI model is better suited to the Slovak quasigeoid model.