# Effect of Surface Mass Loading on Geodetic GPS Observations
## 3 Results and Discussion  
### Root Mean Square Analysis and Correlation Analysis  
Given that the mass loading behaves in the vertical direction, we only considered the vertical component in the following analysis.  
Figure 2 shows the time series of GPS heights of four stations along with AOH-derived vertical displacements. It is clear from Figure 2 that GPS heights and AOH displacements prominently have an annual variation pattern. AOH displacements track GPS heights well at the ANKR, BOR1 and LHAZ sites, indicating that AOH may be responsible for the non-linear vertical motion of GPS stations. However, for the KUNM site, the AOH deformation signal is not in agreement with GPS height signal due to the phase asynchrony between these two time series.  
From Table 2, we can see that the RMS value of GPS height time series varies from 5.8 to 14.5 mm, whereas the RMS value of AOH deformation time series ranges from 3.1 to 7.7 mm. Therefore, AOH cannot fully explain GPS height fluctuations. The Pearson correlation analysis was employed to investigate the correlation between GPS heights and AOH displacements.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Site** & **RMS (GPS)** & **RMS (AOH)** & **Site** & **RMS (GPS)** & **RMS (AOH)** & **Site** & **RMS (GPS)** & **RMS (AOH)** \\ \hline ANKR & 7.6 & 5.3 & KUNM & 8.4 & 6.7 & TASH & 10.7 & 7.5 \\ ARTU & 11.2 & 6.1 & LHAZ & 6.1 & 4.4 & TEHN & 6.3 & 3.9 \\ BII & 8.7 & 6.2 & NOVM & 14.5 & 8.9 & TISE & 6.3 & 5.2 \\ BIFS & 8.2 & 6.2 & NRIL & 8.6 & 5.7 & UKUM & 8.4 & 5.9 \\ BOR1 & 6.7 & 4.3 & ONSA & 6.1 & 5.1 & VILL & 8.5 & 8.3 \\ CHAN & 9.3 & 6.6 & PADO & 5.8 & 4.3 & WUHN & 8.5 & 7.4 \\ CHUM & 9.1 & 6.0 & POLV & 9.0 & 5.2 & YAKT & 8.4 & 7.2 \\ CRAZ & 7.7 & 5.6 & POTS & 8.7 & 6.6 & YEBE & 6.3 & 5.2 \\ IRKT & 11.1 & 8.2 & SHAO & 6.5 & 6.3 & ZECK & 7.9 & 4.9 \\ KIRU & 10.3 & 8.3 & SOFI & 10.0 & 8.9 & ZWE2 & 9.9 & 6.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The RMS value of GPS height time series and AOH deformation time series respectively.  
Figure 2: GPS height time series (blue) and atmospheric, oceanic and hydrological loading (AOH) deformation time series (pink) for (**a**) Ankara, Turkey (ANKR); (**b**) Borowiec, Poland (BOR1); (**c**) Kunming, China (KUNM); and (**d**) Lhasa, China (LHAZ).  
As shown in Figure 3a, GPS height and AOH deformation are positively correlated for all the selected sites, while GPS height and AOH deformation have a strong correlation for most sites (correlation coefficient is greater than 0.6). The strong correlation between GPS heights and AOH displacements may be attributed to the significantly related annual signal. Apart from the annual component, the other components in AOH deformation may act as the potential candidates for determining the strong correlation between GPS heights and AOH displacements. Therefore, by adopting the least squares method, the annual term was removed from GPS heights and AOH displacements to generate GPS height residuals and AOH deformation residuals, respectively. Figure 3b presents the correlation coefficients between GPS height residuals and AOH deformation residuals. All the selected sites are positively correlated, and most sites have a medium correlation (correlation coefficient is between 0.4 and 0.6). Therefore, the correlation between GPS height and AOH deformation is reduced after removing the annual signal.