# Analysis of GNSS Displacements in Europe and Their Comparison with Hydrological Loading Models
## 4 Discussion
### Model Phase Advance over GNSS Seasonal Signal  
The phase advance of the loading models over GNSS displacement could be linked to a single shortcoming of most global hydrology models: the misrepresentation of horizontal fluxes. In general, vertical fluxes are well modelled within each individual cell of the model, but any horizontal runoff often immediately disappears in the oceans. In reality, this water is still stored for a certain time over land and flows through rivers. Examples of the importance of the surface water runoff when computing hydrological loading can be found in [78; 79]. Figure 9 shows that the spatial distribution of this phase advance is not compatible with such a hypothesis because there are no long rivers in Great Britain, but it can play a role in other regions of the world (the Amazon basin, for example, [78]) and has to be carefully investigated. Globally, there is a good match between the models and the GNSS, as the differences between them for the majority of stations are of the same order of magnitude as the GNSS uncertainties (Figure 7). Nevertheless, the differences in phase values confirm that the GNSS annual cycle actually contains signals other than just those from hydrology. If we consider that the agreement between GNSS and the models is good when the histogram of the difference is close to a centred Gaussian distribution (which should indicate random errors), the agreement between GNSS and GLDAS2.1 seems worse than the agreement between GNSS and MERRA2, which seems worse than the agreement between GNSS and GRACE. This result shows the importance of dedicated gravity missions, such as GRACE and GRACE-FO, in helping to improve the modelling of continental water storage variations. The stations where the difference is similar for each loading model are stations where the GNSS annual term contains phenomena other than just the hydrological signature. For example, we did not take into account the nontidal ocean and atmospheric loading [9; 80; 81] in the loading models that we used here. Indeed, the associated annual cycle is quite small in Europe (\(\sim\)0.5 mm) but could explain some  
Figure 12: Coefficient of correlation between annual solar wave and draconitic first harmonic for cosine and sine terms of _tiasd_ as a function of the length of the time series.  
local differences that we see in Figure 9, mostly along the coast. Given the amplitude of the differences, they could also be due to the nature of the ground (karst aquifers [26] and mining [30; 31]), but also to the thermal deformation of the surface and antenna monuments [27; 28]. A meticulous study of each station time series should provide initial intuition into the sources of these differences, but this goes far beyond the goal of this study. In any case, we can observe that groups of stations at large spatial scales that have similar differences are expected to be more likely affected by a geophysical signal, while anomalies on isolated stations are expected to be more likely due to monumentation deformation or a multipath effect. Unlike the thin peaks corresponding to the annual solar frequency in the loading model periodograms of Figure 11, the large peaks centred on the annual solar cycle in the GNSS periodograms are another important piece of evidence for the multiplicity of annual signal content in GNSS.