## 4 Results and Discussion
### Wavelet Transform Results  
#### 4.2.1 CWT Result  
We conducted CWT on the rainfall, reservoir water level, and nonlinear deformation components of feature points to show their time-frequency features. The CWT is expressed as a two-dimensional graph, i.e., continuous wavelet power spectrums with two axes as the proxies of time instant and period (or frequency) of the specific pattern (Figure 11). Therefore, a location with a high modulus value in the CWT generally indicates a localized signal that significantly resembles the frequency-specific wavelet.  
Figure 9: Graph of rainfall, reservoir water level, and nonlinear deformation component of feature points.  
Figure 11: CWT results for different time series data: (**a**) rainfall, (**b**) reservoir water level, (**c**) nonlinear deformation component of P1, (**d**) nonlinear deformation component of P2, (**e**) nonlinear deformation component of P3. The colors in the figure represent the strength of the wavelet power spectrum, with red and blue indicating the peak and valley values of the energy, respectively. The thick black contours indicate the 5% significant level against red noise. The areas with half-transparent masks designate the cone of influence (COI), where the results are unreliable due to the non-negligible edge effects. We use the same layout for Figures 11–13.  
Figure 10: Reservoir water level and vector displacement of GPS monitoring points from 2009 to 2014.  
It has been ascertained from the continuous wavelet power spectrum that there is a period of significance of approximately 1 year (30 \(\times\) 12 days) for both rainfall and feature point P2 throughout the temporal domain of 2016 to 2019, as depicted in Figure 11a,d. Furthermore, the reservoir water level demonstrates a period of significance of approximately 1 year between January 2017 to August 2019, as illustrated in Figure 11b. Similarly, feature point P1 displays a prominent period of around 1 year from January 2016 to July 2017, as portrayed in Figure 11c. Compared to other data, it should be noted that feature point P3's periodicity of around 1 year is not particularly pronounced, even though there is noticeably high energy density in the power spectrogram (Figure 11c).  
In Figure 11a, the peak signal exhibiting a periodicity of 0-48 days appeared in June of 2016, 2017, and 2018, as well as in September of 2019. This may be related to the seasonal precipitation occurring predominantly during summer in the Laxiwa region. A similar phenomenon appears in Figure 11b, where the peak signals of days 0-48 and 72-120 occurred around June of each year, which are likely related to the fluctuations in the water level of the reservoir that could themselves have been caused by flood control, power generation, and irrigation operations at the Laxiwa hydroelectric station. Furthermore, notable power signals with a periodicity of 1-3 months are observed in Figure 11c-e. The underlying causes of these signals require further explanation.  
Figure 12: XWT results for different time series data: (**a**,**c**,**e**) denote the cross-wavelet power spectrum of precipitation and nonlinear deformation of feature points p1, p2 and p3, respectively; (**b**,**d**,**f**) denote the cross-wavelet power spectrum of reservoir water level and nonlinear deformation feature points p1, p2 and p3, respectively. The arrow pointing to the right shows a positive correlation, whereas the arrow pointing to the left represents a negative correlation, for a more detailed explanation of the arrows, please refer to Figure 3.