# Effect of Surface Mass Loading on Geodetic GPS Observations
## 3 Results and Discussion
### Wavelet Coherence Analysis  
Considering that the Pearson correlation analysis is aimed to simply find a correlation in the time domain, there are several issues in determining the specific relationship between GPS heights and AOH displacements with this analysis. Firstly, since the annual component plays an essential role, a more detailed insight aimed at the annual scale (frequency) should be considered. Secondly, in addition to the annual component, other components may potentially be relevant. Lastly, the relationship (e.g., correlation coefficient and relative phase) may change over time. Here, we propose to employ the WTC to overcome all the above-mentioned issues. The WTC spectrum of GPS height time series and AOH deformation time series for the BOR1 site and KUNM site are shown in Figure 4. The reason that we chose these two stations is that Figure 1 displays the approximate relative phase between GPS heights and AOH displacements for the BOR1 site and KUNM site, which can be used to validate the results of WTC. The thick contour indicates the 95% confidence interval against the red noise, while the phase of the area within the cone of influence was unaccounted for due to the edge effects. The relative phasing relationship is denoted by arrows (with in-phase pointing right, anti-phase pointing left and GPS height leading AOH deformation to 90\({}^{\circ}\) pointing straight down). Figure 4 shows that the correlation between these two time series is considerably high at a frequency that is closest to 1 cycle per year (cpy). From Figure 4a, we can see that GPS height time series and AOH deformation time series are in phase at the period closest to 1 year for the BOR1 site, indicating that AOH is responsible for the annual fluctuation in GPS heights. From Figure 4b, we can see that GPS height time series and AOH deformation time series are not in phase at the period closest to 1 year for the KUNM site, indicating that AOH is not responsible for the annual fluctuation in GPS heights. For the high-frequency components (in the period band of fewer than 256 days), although a locally significant correlation was detected, the relative phase angles of the high-frequency components fluctuated sharply, indicating that the GPS height signal and AOH  
Figure 3: (**a**) Correlation between the GPS height and the AOH deformation; (**b**) Correlation between the GPS height residuals and AOH deformation residuals. deformation signal are not in phase. Consequently, it is demonstrated that the geophysical effects cannot explain the sub-seasonal oscillations in GPS observations [23]. Since the fluctuation range of the time-variable relative phasing at the period closest to 1 year is small, the mean WTC-based semblance was computed to quantitatively express the relative phase between these two signals. Following the same method as depicted in Figure 4, the WTC was used to analyze the relative phase between GPS height time series and AOH deformation time series for the other sites, with the mean WTC-based semblance at the frequency closest to 1 cpy. As shown in Figure 5, the average value of the WTC-based semblance for most, but not all, sites are close to 1, indicating that AOH is not a complete representation of the driving force for the non-linear GPS site motion. From Figure 5, we can see that for the SHAO site, the mean semblance is only 0.4, while the other 10 sites (NILI, BJFS, CHAN, KUNM, ONSA, PQTS, SOFI, URUM, VILL and WUHN) have a mean semblance value that is close to 0.7-0.9. Other geophysical effects (e.g., groundwater), GPS systematic errors (e.g., inaccurate local multi-path and tropospheric modelling) and AOH modelling errors (e.g., interpolation method) can lead to the phase asynchrony between GPS observations and mass loading displacements. A measure of RMS reduction ratio expressed in percent (ARMS%) is employed to quantify the correction performance of AOH models:  
Figure 4: The wavelet coherence (WTC) spectrum of GPS heights and AOH displacements for (**a**) BOR1 site and (**b**) KUNM site.