# Analysis of GNSS Displacements in Europe and Their Comparison with Hydrological Loading Models
## 4 Discussion
### Importance of Draconitic Adjustment  
Although it is very common to see GNSS time series adjusted with only the trend and solar cycle, we emphasise here the importance of additionally fitting draconitic harmonics. The differences can be larger than the uncertainty level. The horizontal velocity uncertainties for a large number of stations almost doubled when the draconitic harmonics are not adjusted (Figure 6 and [15]). Even if the numerical estimations of velocity are close in _cats_d_ and _cats_, estimating the draconitic periods, or not, could statistically affect the estimated velocity. The vertical component is less affected since the relative power of the draconitic oscillations is lower than that for the horizontal component, as can be seen in the periodograms in Figure 11. If we look at the annual cycle determination, the draconitic signals influence not only the uncertainties but also the values of the phase and amplitude. Even though these differences and the parameter uncertainties are of the same order of magnitude for the majority of stations, there are several stations for which the annual cycle is strongly affected by the draconitic adjustment. In fact, the separation between the solar annual and first draconitic frequencies in the estimation process is conditioned by the length of the time series. The minimum theoretical length for good separation is 25 years. Even though some of the GNSS time series are close to this duration criterion, we are still not able to properly separate the two components for the majority of stations. Moreover, there is actually no evidence that both solar and draconitic signals are stationary. There are potential amplitude variations over time, especially because of their relation to environmental changes, orbit calculation, and the contribution of local effects such as multipath, which is closely related to the time-variable antenna environment and observation geometry. A clean separation of the two signals could then be even more difficult, even for the longest records. To evaluate the correlation between these two terms, we plot the correlation coefficient values depending on the length of the time series, shown in Figure 12. We represent only the correlation coefficient for the annual/draconitic cosine and sine terms of _tiasd_ that we extracted from Python's WLS estimation function. We chose to only represent the correlation coefficient for the vertical component of GNSS since we previously verified that it was extremely similar for the East and North components.  
The correlation between the solar and draconitic cycles increases when the time series length increases from 4 to \(10\,\mathrm{y}\). For longer time spans, the correlation decreases slowly and linearly.  
The correlation coefficients of the low time span stations (<10 y) are impacted by a large dispersion. The low values of these coefficients are then relatively not significant and should not be misinterpreted. As we suggested before, the parameters of the longest time span stations (19 y) are still correlated (around 0.4). Extrapolating a decorrelation slope (\(-0.02\,\mathrm{y}^{-1}\)) for longer time spans, we found that the total decorrelation between the two cycles should happen beyond a 25-year time span (the theoretical limit), which confirms the difficulty of separating these signals, as they can change with time. In conclusion, even though the correlation between the solar annual and the first draconitic term is quite important, it is strongly recommended to include draconitic frequencies in the fit model in order to reduce the uncertainties, to avoid a joint beat frequency (which can create the illusion of no stationary annual amplitude) being unmodelled, and to try not to mix geophysical signals (mostly at solar frequency) and signals coming from orbital errors.