# Analysis of GNSS Displacements in Europe and Their Comparison with Hydrological Loading Models
## 3 Results
### Tectonic Velocity  
The velocity maps of _cats_d_ are presented in Figure 4. We used two scales (red and green arrows) in the horizontal map to distinguish the largest velocities in Greece and Turkey, while the yellow dots represent the stations with horizontal velocities lower than \(1\,\mathrm{mm}/\mathrm{y}\). In order to provide the horizontal velocity field relative to the Eurasian plate, we removed the rotation of the Eurasian plate with the Euler pole coordinates estimated in [67] (\(\mathrm{lon}_{\mathrm{p}}=-99.094(7)^{\circ}\mathrm{E}\), \(\mathrm{lat}_{\mathrm{p}}=55.070(4)^{\circ}\mathrm{N}\), \(\omega=0.261(1)\times 10^{-6}\,\mathrm{deg}/\mathrm{y}\)). This enabled us to compare our solution with previous regional studies [1] or the EPOS (European Plate Observing System) solution available at [[http://doi.osug.fr/data/public/GNSS_products/Europe/](http://doi.osug.fr/data/public/GNSS_products/Europe/)]([http://doi.osug.fr/data/public/GNSS_products/Europe/](http://doi.osug.fr/data/public/GNSS_products/Europe/)) (accessed on 7 November 2021). The vertical velocity map is represented together with the ICE-6G_D GIA model developed by [68; 69]. In general, there is a good match between the two, although some differences are noticeable, especially in Southern Italy, where other non-GIA geophysical signals may occur. In Figure 5, we provide the velocity differences between _cats_d_ and _cats_, _cats_d_ and _tiasd_, and _cats_d_ and _epos_. We observe that there are no significant differences between the velocity values of the two CATS estimations, while _tiasd_ slightly underestimated the vertical velocities compared to _cats_d_. The distribution shown by the histogram remained Gaussian for both vertical velocity differences. Moreover, we do not observe any preferential direction \begin{table}
\begin{tabular}{l c c c} \hline \hline  & _cats_d_ & _cats_ & _tiasd_ \\ \hline Draconitic frequencies adjustment & Yes & No & Yes \\ Interannual variation & – & – & polynomials \\ Stochastic model & WH + PL noise & WH + PL noise & WH noise \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Estimation properties of the three models considered in this article. Figure 4: Velocity field of _cats_d_ in (**a**) horizontal and (**b**) vertical direction, along with ICE-6G_D GIA model of [68]. The yellow dots in (**a**) are stations for which the horizontal velocity is lower than \(1\,\mathrm{mm}/\mathrm{y}\). in the horizontal maps, such that we can make two assumptions. The first is that none of the estimation methods seem to be biased with respect to the others. The second is that we can consider the velocity differences as a random field. In order to compare our GNSS solution to other published GNSS solutions, we chose to compute the difference between _cats_d_ and the EPOS solution for the common stations, as both networks are slightly different. We see that there are some systematic effects on both components, especially for the vertical component, whose distribution is shifted near \(0.5\,\mathrm{mm}/\mathrm{y}\). These effects, being visible at large spatial scales, probably indicate a difference in reference frame realisation. In fact, the reference frames of the two solutions are obviously different since the IGS_R3 reference frame is specifically used in REPRO3 products. Nevertheless, when we removed this mean shift, the distribution seemed to follow the same behaviour as _cats_d_-_tiasd_ (_cats_d_ slightly overestimates the velocity compared to _tiasd_ and _epos_). Figure 5: **(a,b)** Difference in velocity field between _cats_d_ and _cats_. The panel **(c)** represents the number of stations where the vertical velocity was, respectively, overestimated (red) or underestimated (blue) by _cats_d_ compared to _cats_. (**d–f**) are the same for the difference between _cats_d_ and _tiasd_, and (**g–i**), between _cats_d_ and the EPOS solution.