## 2 Materials and Methods
### GNSS Time Series in Height Component  
The time series analyses were performed for two main purposes: first, to make predictions for the future by explaining the past with the help of observation values from past periods. The second purpose is to determine the effect of any effective factor in the series. This effect can be a momentary event or a set of events spread over a certain time period. This way, the degree of impact is determined, measures are taken, or regulations are made for the future. Some changes and irregularities can be seen in the series. These changes and irregularities were caused by four factors (components) and there were differences in the direction and intensity of their effects. These are trend, seasonality, cyclicality, and noise [34; 35]. The time series of the GNSS stations are obtained from daily processes. Linear, periodic, and irregular movements of reference stations can be determined by time series analysis. The time series of these reference stations can be written for the horizontal and vertical components as follows [36; 37];  
\[\overline{x}(t_{i})=\sum_{k=1}^{m}a_{k}t_{i}^{k-1}+\sum_{s=1}^{r}[b_{s}\text{ cos}(2\pi f_{s}t_{i})+c_{s}\text{sin}(2\pi f_{s}t_{i})]+\sum_{j=1}^{p}\alpha_{j} \overline{x}(t_{ij})+\sum_{j=1}^{q}\beta_{j}\varepsilon(t_{ij})+\varepsilon(t _{i}) \tag{1}\]  
where \(a_{k}\) is the trend component parameter, \(b_{s}\) and \(c_{s}\) are the amplitude of periodic signals, \(f_{s}\) is the corresponding frequency, \(\alpha_{j}\) is the autoregressive \(AR(p)\) model parameter, \(\beta_{jj}\) is the moving average \(MA(q)\) model parameter, and \(\varepsilon(t)_{i}\) is the residual (noise) to which we pay more attention. The trend component in the time series represents the time-dependent long-period changes [38]. The Least Squares Method (LSM) separates the trend component from the series in the time series. However, LSM cannot predict the parameters of the time series components in the equation with outliers. The main disadvantage of LSM is its sensitivity to outliers [36]. An outlier is an observation that significantly deviates from other observations in the sample [39]. Outliers should be removed from the time series before starting the analysis. Figure 1: Locations of GNSS stations. Outliers in the time series were investigated using a robust method. According to the predicted model, outliers were determined and removed from the time series, the gaps in the data were calculated, and the time series were reconstructed [40]. Outliers in time series were eliminated from the series by using Bi-square weighted robust predictor methods. New values were determined for the eliminated values in the series. Also, the loss of data can be determined by this method. Bi-square weights minimize a weighted sum of squares, where the weight given to each observation point depends on how far the point is from the fitted line. Points near the line get full weights, whereas points far from the line get reduced weights. Robust fitting with Bi-square weights uses an iteratively re-weighted LS algorithm and follows the weight function [40]. The weight functions of robust estimators in Bi-square are:  
\[w_{i}= \begin{cases}\left[1-\left(\frac{\gamma_{i}}{r}\right)^{2}\right]^{2}& for\ |v_{i}|\leq r\\ 0&for\ |v_{i}|>r\end{cases} \qquad r=4.685 \tag{2}\]  
where \(r\) is a tuning constant equal to 4.685. Outliers from the observations were removed, and the gaps were determined using the model. Subsequently, the series was reconstructed. Figure 2 shows that the new dataset for the RZE1 height is compatible with the raw dataset. In Figure 2, the black lines represent the raw data, the red stars denote the outliers, and the blue lines illustrate the new dataset with the outliers removed. Then, the Fast Fourier Transform (FFT) was applied to the height time series to calculate the frequencies and corresponding period values where the trend component was removed [41]. Since the peak values in the graphs vary, the frequency range was adjusted to ensure graph suitability.