## 4 Results and Discussion
### CEEMDAN Decomposition Results  
The final prediction accuracy of the MC-TCGRU model is closely related to the sequence decomposition and prediction process within the model. Therefore, it is essential to analyze the characteristics of the different components in the time series. The complete set of subsidence sequence data was decomposed using the CEEMDAN algorithm, and the decomposition results of the five InSAR LS sequences in Kunming are shown in Figure 7a-e. Each subsidence time series was decomposed into four components: three intrinsic mode functions (IMF\({}_{1}\), IMF\({}_{2}\), and IMF\({}_{3}\)) and a residual component. The frequency of data fluctuations decreases progressively from IMF\({}_{1}\) to the residual component, and the patterns of change became simpler compared to the original sequence. Figure 7: CEEMDAN decomposition results for 5 LS points. (**a**) P1; (**b**) P2; (**c**) P3; (**d**) P4; and (**e**) P5. Each decomposed component reflected different fluctuation information within the subsidence sequence data. The IMF\({}_{1}\) component showed the most significant fluctuations, with a less regular pattern, indicating a highly uneven distribution of subsidence values. As the decomposition progressed, the volatility of the subsequence curves decreased, gradually becoming more linear, with the residual component being the smoothest. The residual component can be considered the trend term of the subsidence sequence, reflecting the main trend of subsidence, which was often caused by regional geological conditions and human activities. The other IMF components, which exhibited obvious periodicity, reflected subsidence due to cyclic factors such as groundwater oscillations and precipitation. The proposed MC-TCGRU model performed predictions on these five InSAR LS time-series data points. After decomposition using the CEEMDAN algorithm, a residual component and multiple intrinsic mode function components were obtained. Due to differences in the complexity and stability of the data, the characteristics of the components obtained from each point often varied. The low-frequency components generated by the CEEMDAN decomposition represent the trend and periodic characteristics of the original data, while the high-frequency components represent the details and noise of the original data. For the InSAR LS data used in this study, the residual component can be regarded as representing the overall trend in LS, which may be related to long-term factors such as the lithology, geological structure, and human activities in the study area. The IMF\({}_{3}\) component in points P1, P3, and P4 showed a cyclical change with a period of about six months, representing a semi-annual subsidence evolution trend, while the IMF\({}_{3}\) component in point P5 had a cycle of about one year, which may be related to cyclic changes in factors such as precipitation and groundwater oscillations. The IMF\({}_{2}\) component had a shorter and more complex cycle, reflecting the detailed variation characteristics of the subsidence sequence. The IMF\({}_{1}\) component was the most complex, containing noise and outliers after data decomposition, with a high degree of randomness, making it the most challenging to predict. In the proposed MC-TCGRU model, the original data were first decomposed using the CEEMDAN algorithm, and the resulting components were individually predicted to obtain the final integrated prediction results. The prediction accuracy of each component directly affected the overall prediction accuracy. Since the data characteristics and range of each component differed, they also had varying impacts on the final prediction results. Taking the point P1 as an example, the prediction results of each component in the test set are shown in Figure 8.  
Among the four components, the residual component curve was the smoothest, with a more linear trend, while the IMF\({}_{1}\) component showed the most significant volatility.