## 3 Results and Discussions
### Noise Analysis  
In this part, we compute the power spectral density (PSD) of the three types of data--original GNSS solutions, GNSS corrected by GGFC solutions and GNSS corrected by GRACE solutions. The Lomb-Scargle periodogram method is applied to detect the noise characteristics in the log-log coordinate system [32; 53; 54]. In order to gain a global view of the PSD variations, all of estimated spectra are stacked by component and are smoothed with a Gaussian smoother using GMT software. Figure 7 shows the filtered PSD stacking results for the three types of solutions. The blue line with a slope of \(-1\) denotes the power-law behavior of flicker noise in the log-log coordinate system. The overall noise behavior is similar for both IG2 solutions and the two types of IG2 combined solutions, and spectra of the flicker noise can describe the variations well for all three types of datasets. The noise characteristics become more and more white with the growing of the frequency. When the frequency expands higher than four cycles per year (cpy), a slope of 0 (white noise) could resemble the background noise well, either due to the intervention of a white noise frequency floor or because of a change in the basic characteristics of the underlying noise process to some type of non-integer power law intermediate between the flicker and white distributions [7; 9; 30]. The results also demonstrate that all three datasets have similar characteristics. The peaks are consistent for the three types of datasets, while the annual (1.0 cpy) is the most dominant frequency in all three datasets, and draconic signals are also obvious for the higher frequencies. However, the PSD amplitudes are different among the three datasets. After correcting GNSS solutions with GRACE- and GGFC-derived non-tidal mass variations, the stacked PSD amplitudes show an obvious decrease trend, especially for the annual frequency. This can be a useful clue to help us reduce some of seasonal signals in GNSS coordinate time series when reprocessing GNSS data corrected by GRACE or GGFC solutions. We quantitatively analyze noise variations of the GRACE- and GGFC-derived non-tidal mass loadings on the global ISS stations. GNSS coordinate time series are assumed to consist of signal plus noise. To describe the signal, a trajectory model, which includes the linear trend, seasonal signals, offsets and post-seismic relaxation, is introduced [55]. The purpose of most GNSS time series analysis is to estimate accurately the parameters within the trajectory model. The residual which comes from subtracting the trajectory model from the observations represents the noise in GNSS time series. To accurately compute noise characteristics of the GNSS time series, the optimal noise model needs to be defined first. Considering that different stations have different noise properties, many  
Figure 7: Stacked periodogram of the coordinate time series. The black vertical lines represent the 1.0 cycle per year (cpy) harmonics, respectively. The power-law behavior of flicker noise is denoted by the blue line with a slope of \(-1\). researchers have carefully investigated the appropriate noise models for different areas. Most recently, according to [55], for global stations, the preferred noise models are the power law (PL) or flicker noise (FN) with white noise (WN). Therefore, we select PL+WN and FN+WN, respectively, as the optimal noise model to describe the noise (residuals) existing in the above three types of data. The Create and Analyze Time Series (CATS) software is applied in the computations and the used trajectory model is a linear trend with an annual and semi-annual signal plus the aforementioned offsets. Figure 8 displays total noise amplitudes (FN+WN) variations after correcting GNSS results with GGFC and GRACE solutions, respectively. For solutions with GGFC loading corrections, the number of stations with noise amplitudes decrease is 120/186, and the mean amplitude variations of stations with noise amplitude decrease and increase are 12.1% and 49.7%, respectively.