# Analysis of GNSS Displacements in Europe and Their Comparison with Hydrological Loading Models
## 3 Results
### Principal Component Analysis of the Interannual Signal  
The interannual signals derived from GNSS and derived from loading models are compared using PCA decomposition. All the time series were previously detrended (using the trend estimate from _cats_d_ for GNSS) and resampled to nearly every 10 days by taking the mean of the successive intervals of the year (01/01-10/01, 11/01-20/01, 21/01-31/01, 01/02-10/02, 11/02-20/02, 21/02-28/02,...). The intervals that contained no data were left empty. Then, we completed the time series using linear interpolation. We chose to treat GRACE time series by keeping the original sampling of one month before interpolation. We finally removed the mean seasonal signal in the same way as [44]. We obtained this cycle by calculating the mean of the collection of the same dates within years: for example, taking the mean of every 05/01, the mean of every 15/01, and so on. This is arguably the best way to filter the mean seasonal cycle compared to a sinusoidal fit. We choose to select stations only based on the following completeness criterion. The selected stations have available data between 2010 and 2020, which have accumulated gaps no longer than 60 days, the largest of which is less than 30 days, and have 90% completeness such that the interpolation should not distort the signal too much. Implementing these criteria left 268 stations from the initial network presented in Figure 3. We call EOFs (empirical orthogonal functions) the spatial function and PCs (principal components) the temporal associated time series of the PCA output. The first three principal components (also called modes) of the residual time series are presented in Figure 10, where we report the variance fraction of the total variance associated with each mode in each panel. We see that the variance fraction of the GNSS is equal to or lower than the models for each mode and that the GNSS's first PCs are much noisier than the ones from the model, even after resampling the data (which removes a part of the GNSS white noise). The first mode is spatially quite homogeneous. The associated PCs are very different between GNSS and the loading models. Among the three models, we can find some common temporal patterns, but also some differences that can be important, especially with GRACE. The second and third modes are under 15% of the variance fraction but show common spatial patterns between the solutions. It seemsthat the two modes have to be interpreted simultaneously since PCs and EOFs belonging to both appear to be very similar. For example, the PCs and EOFs of panels (i), (f), (g), and (l) seem to be consistent when they belong to two different modes (the same is the case for (j), (k), and (h)).  
Figure 9: Differences in phase and amplitude of annual solar cycle and the associated histograms as described in Figure 8 between _cats_d_ and GLDAS2.1 **(a–d)**, MERRA2 **(e–h)**, and GRACE **(i–l)**.  
Figure 10: PCA (EOFs and associated PCs) of GNSS and the three loading models’ (including GRACE) residual time series between 2010 and 2020, where the trend and the seasonal signal have been removed: (**a–d**) first component, (**e–h**) second component, and (**i–l**) third component. The percentage of the total variance corresponding to each mode is given in each plot. The PCs are scaled to unit variance and plotted for the period 2010 to 2020, while the corresponding EOFs are given in terms of the correlation between the initial time series and the PCs.