## 3 Methodology
### Evaluation Metrics  
In the present study, six evaluation metrics, namely the mean absolute error (MAE), mean square error (MSE), mean absolute percentage error (MAPE), normalized root mean square error (NRMSE), coefficient of determination (R\({}^{2}\)), and Kling-Gupta efficiency (KGE), were applied to evaluate the model performance. These evaluation metrics are defined as follows:  
\[\text{MAE}=\frac{1}{N}\Bigg{(}\sum_{t=1}^{N}\big{|}y_{pre,t}-y_{obs,t}\big{|} \Bigg{)} \tag{19}\]  
\[\text{MSE}=\frac{1}{N}\sum_{t=1}^{N}\big{(}y_{pre,t}-y_{obs,t}\big{)}^{2} \tag{20}\]  
\[\text{MAPE}=\frac{1}{N}\Bigg{(}\sum_{t=1}^{N}\bigg{|}\frac{y_{pre,t}-y_{obs,t} }{y_{obs,t}}\bigg{|}\Bigg{)}\times 100\% \tag{21}\]  
\[\text{NRMSE}=\frac{1}{\overline{y}_{obs}}\sqrt{\frac{\sum_{t=1}^{t}\big{(}y_ {pre,t}-y_{obs,t}\big{)}^{2}}{N}} \tag{22}\]  
where \(N\) is the quantity of deformation monitoring data; \(y_{obs,t}\) presents the measured values of landslide displacement; \(y_{pre,t}\) is predicted values of landslide displacement; \(\overline{y}_{obs}\) and \(\overline{y}_{pre}\) represent the mean values of observations and predictions; \(\mathbf{r}\) is the linear relative coefficient between simulated displacement values \(y_{pre,t}\) and observed displacement values \(y_{obs,t}\); \(\alpha=\sigma_{y_{pre}}/\sigma_{y_{obs}}\) is a metric of the relative variability between predicted and observed  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Parameters** \\ \hline EMD & Maximum value of siftings as an ending standard = 10 \\ \hline EEMD & \begin{tabular}{c} Maximum value of siftings as an ending standard = 10; \\ Quantity of copies of the original signal to use as the ensemble = 200 \\ Value of additional noise = 0.2 \\ Maximum number of parallel threads = 1 \\ \end{tabular} \\ \hline RNN & \begin{tabular}{c} Learning rate = 0.6 \\ Neuronic quantity in hidden layer = 55 \\ Maximum value of interactions = 1000 \\ \end{tabular} \\ \hline GRU & \begin{tabular}{c} Learning rate = 0.5 \\ Neuronic quantity in hidden layer = 50 \\ Maximum value of interactions = 400 \\ \end{tabular} \\ \hline LSTM & \begin{tabular}{c} Learning rate = 0.7 \\ Neuronic quantity in hidden layer = 50 \\ Maximum value of interactions = 1000 \\ \end{tabular} \\ \hline SVM & \
\begin{tabular}{c} Penalty factor = 0.1 \\ Kernel function parameter = 3 \\ Tolerance of termination criterion = 0.001 \\ \end{tabular} \\ \hline ELM &
\begin{tabular}{c} Neuronic quantity in hidden layer = 20 \\ Random seed = 1 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameter settings in the comparative studies.  
displacement; and \(\beta=\mu_{y_{pre}}/\mu_{y_{obs}}\) is the ratio between the average predicted displacement to the average observed displacement. The MAE is the average of the absolute errors between the predicted values and actual values, which reflects the actual predicted value error. The MSE is the expected value of the square of the difference between the predicted values and actual values, which evaluates the degree of variability in the data. The MAPE further considers the radio between error and the actual value. In general, the smaller the MAE, MSE, and MAPE values, the better the model performs. The NRMSE allows to read the errors in a more understandably way, since it is a non-dimensional parameter. The R\({}^{2}\) measures the linear relationship between the predicted values and actual values of a dependent variable, whereby a high value of R\({}^{2}\) (up to one) signposts a perfect model. The KGE values range from negative infinity to 1. It can evaluate the model performance from three perspective views: Correlation, bias, and variability [51; 52]. For an ideal prediction model, the value of KGE should be as close to 1 as possible.