# Analysis of GNSS Displacements in Europe and Their Comparison with Hydrological Loading Models
## 1 Introduction  
Time series of station coordinates derived from global navigation satellite systems (GNSS) have been used for decades to investigate various geophysical phenomena. Horizontal components have mostly been used to estimate tectonic activity (plate motion [1; 2]) or seismic events [3; 4]), and vertical components have been used for seasonal signals due to mass redistribution (hydrological loading [5; 6; 7]), atmospheric loading [8], nontidal ocean and atmospheric loading [9], and ice-snow loading [10; 11]). All components are also used to determine reference frames, such as the International Terrestrial Reference Frame (ITRF) [12]. Aside from these signals, GNSS position time series also contain large broadband variations of unknown origin, typically represented by the combination of power-law (PL) and white noise (WH) models [13], which impacts the determination and interpretation of other parameters, especially the velocity and its uncertainty [14; 15; 16], but also possibly the seasonal signal [17]. The origin of PL noise in GNSS position time series may have several sources: orbit mismodelling [18], tropospheric delay [19], instability of the station monumentation [20; 21], and multipath [22], etc. Moreover, [23] shows that the assessmentof noise content in GNSS position series is heavily impacted by the estimation of position discontinuities, which make the interpretation even more difficult and compromise the validity of long station records. Taking into account that the broadband noise variations are also correlated spatially [24; 25], the proper interpretation of the interannual variations in GNSS position time series and their common modes across a region remains a challenging task. The deformations that are observed in GNSS position time series may depend not only on the geological nature of the crust (karst aquifers [26]) and its thermal deformation [27; 28] but also on human activities (groundwater pumping [29] and mining [30; 31]). We can suspect some apparent deformation related to the stability of the station monument. Finally, in [32], the authors show that the power spectral density (PSD) from GNSS position time series contains harmonics of 1.04 cpy (cycle per year), known as the GPS draconitic oscillation. The origin of the draconitic oscillation and its harmonics in GNSS time series is still not well established but is most likely due to satellite orbit mismodelling [32; 33]. The first draconitic harmonic is very close to the annual solar cycle (1 cpy), so the estimated amplitudes of these two waves are strongly correlated. Thus, the interpretation of the seasonal signal, and especially the annual signal, is highly dependent on the draconitic signal estimation. In this study, we used specific IGS REPRO3 GNSS satellite orbit and clock products computed by the CNES-CLS team on behalf of the Groupe de Recherche en Geodesie Spatiale (GRGS, [[https://grgs.obs-mip.fr/](https://grgs.obs-mip.fr/)]([https://grgs.obs-mip.fr/](https://grgs.obs-mip.fr/)) (accessed on 7 November 2021) ) in France. They were used to calculate station positions in precise point positioning (PPP) mode using the GINS software developed by CNES [34]. We computed the daily position solutions of more than one thousand stations mainly located in Western Europe and Scandinavia. We extracted the linear velocity and seasonal signals together with their uncertainties to validate the accuracy of the estimation of the new products using different methods. We also assessed the spectral contents of the time series, especially in terms of the noise level at the interannual band. Among the current techniques used for determining the parameters of the model, we can cite the weighted least squares method (WLS), Kalman filtering, (multi-) singular spectrum analysis (M-SSA), and the Wiener filter, all reported and analysed in [35]. We demonstrated the importance of the contribution of the interannual variation in GNSS time series by using two different methods of estimation.