## 4 Research Results
### Assessment of the Accuracy of the Gravity Values and height Anomalies Determined from the GGI Model
This is probably related to the methods used for construction of both quasigeoid models. In the process of developing the Polish quasigeoid model, gravity data were not used directly (this is the EGM2008 model fitted to the GNSS/levelling points [27]). Thus, the presented differences may indicate greater accuracy for the Slovak quasigeoid model. However, this is only a suggestion, of which the results are not settled. In order to investigate the significance of the constant density zones dimensions to the accuracy of the model, calculations were carried out by assuming zones of constant density in used earlier \(4\times 4\) km and three additional versions: \(8\times 8\) km (900 constant density zones), \(6\times 6\) km (1600 constant density zones), and \(3\times 3\) km (6400 constant density zones), with all other parameters left unchanged. Constant density zones dimensions are presented in Figure 4. Table 3 presents the results of these calculations, giving statistics for all test points. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Test Points Group** & **EGM08** & \(\mathbf{1\times 1}\)**km** & \(\mathbf{0.5\times 0.5}\)**km** & \(\mathbf{0.25\times 0.25}\)**km** & \(\mathbf{0.1\times 0.1}\)**km** & **Average Height [m]** \\ \hline \multicolumn{7}{c}{Stdev(\(\Delta\zeta\)) [cm]} \\ \hline All test points & 2.64 & 2.15 & 2.18 & 2.20 & 2.26 & 447 \\ \hline \multicolumn{7}{c}{Stdev(\(\Delta\)g) [mGal]} \\ \hline \(H_{I}\) & 2.95 & 0.90 & 0.70 & 0.65 & 0.68 & 237 \\ \(H_{II}\) & 8.49 & 1.56 & 0.99 & 0.91 & 1.05 & 473 \\ \(H_{III}\) & 13.80 & 1.63 & 1.00 & 1.03 & 1.29 & 838 \\ All test points & 8.75 & 1.38 & 0.90 & 0.85 & 0.98 & 438 \\ \hline \end{tabular}
\end{table} 
Table 1: Standard deviations of differences \(\Delta\zeta\) and \(\Delta\)g for different DEM resolutions. The Polish part: \(\rho_{0}=2670\) kg/m\({}^{3}\), constant density zones with dimensions \(4\times 4\) km. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Test Points Group** & **EGM08** & \(\mathbf{1\times 1}\)**km** & \(\mathbf{0.5\times 0.5}\)**km** & \(\mathbf{0.25\times 0.25}\)**km** & \(\mathbf{0.1\times 0.1}\)**km** & **Average Height [m]** \\ \hline \multicolumn{7}{c}{Stdev(\(\Delta\zeta\)) [cm]} \\ \hline All test points & 3.15 & 0.90 & 0.86 & 0.95 & 0.98 & 826 \\ \multicolumn{7}{c}{Stdev(\(\Delta\)g) [mGal]} \\ \(H_{I}\) & 6.48 & 1.85 & 1.11 & 0.87 & 0.89 & 260 \\ \(H_{II}\) & 12.05 & 1.80 & 1.02 & 0.83 & 0.89 & 545 \\ \(H_{III}\) & 18.63 & 2.17 & 1.28 & 1.10 & 1.19 & 940 \\ All test points & 16.24 & 2.00 & 1.16 & 0.98 & 1.06 & 746 \\ \hline \end{tabular}
\end{table} 
Table 2: Standard deviations of differences \(\Delta\zeta\) and \(\Delta\)g for different DEM resolutions. The Slovak part: \(\rho_{0}=2670\) kg/m\({}^{3}\), constant density zones with dimensions \(4\times 4\) km. Taking into account the height anomalies, it should be stated that there is no dependency of the accuracy of their determination on the analyzed dimensions of the constant density zones. Again, there are differences in the accuracy of determining gravity. Only for the two versions, the used earlier \(4\times 4\) km and smaller \(3\times 3\) km, these accuracies are the highest (approximately 1 mGal). Enlarging the zones of constant densities visibly reduces the accuracy. 1.2 The Impact of the Density of the Gravity Data and the Initial Density of Topographic Masses Model on the Determined Gravity Values and Comparison with the Classical Methods of Gravity Prediction  
The high accuracy of gravity obtained from GGI models shown earlier (Tables 1-3) is also the result of the very high density of gravity data used in the calculations. Along with the decreasing number of data points, the accuracy of the model should be expected to decrease. The estimation of the influence of gravity data density on the accuracy of the model in terms of height anomalies was initially estimated by [13]. We will now focus on assessing the accuracy of the gravity.