# Analysis of GNSS Displacements in Europe and Their Comparison with Hydrological Loading Models
## 3 Results
### Annual Signal  
We now focus on the annual solar cycle of the time series derived from the three estimated solutions. Among the known sources of seasonal variations in GNSS position time series, we can cite the hydrological loading of amplitude \(\sim\)4 mm in Europe [70], thermoelastic deformation of the crust of amplitude \(\sim\)1 mm [27; 28], nontidal loading of amplitude \(<\) 1 mm in Europe [9], and thermal dilation of the GNSS monumentation with variable amplitudes.In addition to the velocity field, the annual cycle recovery also depends on the choice of the estimation method. Figure 7 represents the phase and amplitude of _cats_d_ for the vertical component with their uncertainties. The horizontal components are not shown here because their amplitudes were at the level of the resolution of the technique (the uncertainties had the same order of magnitude as the signal) and could have been dominated by GNSS monument motion, which makes the interpretation very difficult. Figure 6: Uncertainty of (**a–c**) horizontal and (**d–f**) vertical velocity field for _cats_d_, _cats_, and _tiasd_. In spite of spatial variations in both amplitude and phase from Figure 7, the results are coherent with the expectations of finding maximum displacement in the mid-summer or beginning of fall, with 3 to 4 mm of mean amplitude. We can observe some typical patterns: for example, a gradient of amplitude over Great Britain and larger amplitudes in Eastern Europe and Scandinavia due to important snow covering (compared to Western Europe) and atmospheric loading signals caused by Siberian anticyclones, both in winter. In addition, the uncertainties are mostly below 1 month for the phase and 1 mm for the amplitude, which make the results suitable for proper interpretation. As for velocities, we compared the results of _cats_ and _tiasd_ with respect to _cats_d_ in Figure 8. The phase differences are coloured in red when the tested model is delayed compared to _cats_d_ and in blue when it is in phase advance. Note that we computed the difference in amplitudes (resp. phase) and not the amplitude (resp. phase) of the  
Figure 7: (**a**) Phase and (**b**) amplitude of _cats_d_ along with their respective uncertainties (**c,d**) estimated using CATS software. The colour bar of the phase map indicates the month of maximum displacement towards the up direction. differences. We will evaluate both the effects of the interannual estimation method and draconitic adjustment in the annual solar cycle recovery. For the difference between _cats_d_ and _cats_, there are two distinct effects resulting from the estimation of the draconic frequencies which affect the amplitude and phase of the annual solar cycle. The first is the small phase delay of _cats_, which has also a smaller amplitude compared to _cats_d_. This is consistent with the fact that the draconitic cycles can disrupt the solar cycle and that the modulation between the draconitic first harmonic and the annual solar oscillation can bias the estimation of the latter. We also remark that the distribution of the differences in the histograms reflects the spatial variability of the draconitic terms. For the difference between _cats_d_ and _tias_d_, there are also two distinct effects resulting from the estimation method of interannual variations which affect the amplitude and phase of the annual solar cycle. We observe that estimating the interannual variations with polynomials seems to increase the amplitude of the annual cycle and to create a slight advance of phase. The distribution of the differences in the histograms is tighter than in the previous case since the spatial variability of the difference is less important. The estimation of the interannual polynomials has opposite consequences on the solar cycle amplitude/phase determination than the estimation of draconitic frequencies, but the differences remain small and near the uncertainty level observed in Figure 7: the majority of stations show differences shorter than a month for the phase and smaller than 1 mm for the amplitude.