## 4 Results and Discussion
### Model Performance Evaluation  
To accurately evaluate the overall predictive performance of the MC-TCGRU model, the STL-based prediction model, the EMD-based prediction model, and the prediction model without time-series decomposition, we calculated the MAE, RMSE, R\({}^{2}\), MAPE, and SMAPE metrics for each model across five LS points. These five AEMs comprehensively assessed the prediction accuracy of the models from multiple perspectives. Table 1 presents the accuracy evaluation results for the four time-series prediction models on the five InSAR LS points, with the best value for each evaluation metric highlighted in bold. According to Table 1, the proposed MC-TCGRU model achieved the best performance across all AEMs on the five LS points, followed by the EMD-TCGRU model and the STL-TCGRU model, with the TCGRU model showing a relatively poorer performance. From the perspective of data differences, the prediction values of the STL-TCGRU and EMD-TCGRU models were relatively underestimated compared to the MC-TCGRU model in point P1 and relatively overestimated in the points P3, P4, and P5. The two models produced similar prediction results for the points P2, P3, and P4, while their results differed significantly for the points P1 and P5, which is related to the varying characteristics of the different points. The MC-TCGRU model showed significant improvements in predicting LS with greater volatility, such as at the values of abrupt change in the point P3, where its performance surpassed that of the TCGRU model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Points** & **Model** & **RMSE** & **MAE** & **R\({}^{2}\)** & **MAPE (\%)** & **SMAPE (\%)** \\ \hline \multirow{4}{*}{P1} & TCGRU & 2.83 & 2.24 & 0.87 & 3.02 & 3.03 \\  & STL-TCGRU & 2.64 & 2.00 & 0.89 & 2.64 & 2.68 \\  & EMD-TCGRU & 2.46 & 2.09 & 0.90 & 2.77 & 2.76 \\  & MC-TCGRU & **2.44** & **1.99** & **0.90** & **2.61** & **2.63** \\  & TCGRU & 2.19 & 1.63 & 0.88 & 2.40 & 2.41 \\  & STL-TCGRU & 2.17 & 1.75 & 0.88 & 2.56 & 2.58 \\  & EMD-TCGRU & 1.92 & 1.52 & 0.90 & 2.20 & 2.24 \\  & MC-TCGRU & **1.67** & **1.28** & **0.93** & **1.84** & **1.85** \\  & TCGRU & 2.50 & 1.86 & 0.29 & 4.61 & 4.66 \\  & STL-TCGRU & 2.25 & 1.73 & 0.43 & 4.37 & 4.37 \\  & EMD-TCGRU & 2.19 & 1.71 & 0.46 & 4.23 & 4.28 \\  & MC-TCGRU & **2.08** & **1.64** & **0.51** & **4.05** & **4.09** \\  & TCGRU & 2.45 & 2.00 & 0.87 & 2.68 & 2.68 \\  & STL-TCGRU & 2.31 & 1.83 & 0.88 & 2.48 & 2.49 \\  & EMD-TCGRU & 2.04 & 1.69 & 0.91 & 2.23 & 2.25 \\  & MC-TCGRU & **1.77** & **1.49** & **0.93** & **1.99** & **2.00** \\  & TCGRU & 2.92 & 2.37 & 0.93 & 1.61 & 1.63 \\  & STL-TCGRU & 3.04 & 2.37 & 0.93 & 1.59 & 1.61 \\  & EMD-TCGRU & 2.90 & 2.23 & 0.94 & 1.47 & 1.47 \\  & MC-TCGRU & **2.41** & **1.99** & **0.96** & **1.34** & **1.34** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The AEMs of different models (a bold value means the best AEM of the column). When examining the TCGRU model's performance across different AMEs, the MAE and MAPE measured the model's absolute error, R\({}^{2}\) assessed the fit of the model's predictions, and the MAPE and SMAPE represented the model's relative error. Together, these metrics provide a comprehensive view of the model's predictive performance. For the RMSE metric, the MC-TCGRU model reduced the error by 13.78%, 23.74%, 16.80%, 27.76%, and 17.47% across the five points compared to the TCGRU model. For the R\({}^{2}\) metric, the MC-TCGRU model improved the fit by 3.45%, 5.68%, 75.86%, 6.90%, and 3.23% across the five points. For the SMAPE metric, the errors were reduced by 13.20%, 23.24%, 12.23%, 25.37%, and 17.79%. Excluding point P3 due to the small magnitude of the R\({}^{2}\) metric, the MC-TCGRU model showed improvements of 0.03, 0.05, 0.06, and 0.03 for the P1, P2, P4, and P5 datasets, respectively, compared to the TCGRU model. The most significant improvement in the predictive accuracy was observed at the P4 point, highlighting the model's enhanced performance at this location.