## 4 Validity of 1D-CNN Bandpass Filter  
We first examine the training process of the 1D-CNN filter model. In each training cycle, the losses (_MSE_) calculated for both training and validation are primarily examined. The correlation coefficient is computed as another metric to verify the performance of the 1D-CNN filter. In the following paragraphs, we take the daily mean temperatures at the HKO, HKA, CCH, and TKL stations as examples to illustrate the validity of the 1D-CNN bandpass filter. Figure 2: Model structure diagram of one-dimensional convolutional neural network. As shown in Figure 3, we find that the model's loss gradually decreases during the training process and converges to a relatively stable state when the iteration count reaches 2000. The effectiveness of training is evaluated comprehensively through the loss curves and correlation coefficient curves mentioned above. A smaller _MSE_ loss and a higher correlation coefficient indicate that the 1D-CNN filter output is closer to the ground truth, implying better training performance of the 1D-CNN filter. Our results show that for the HKO site, the correlation coefficients between the 1D-CNN and Lanczos filter outputs for the training set and the validation set are approximately 0.9977 and 0.9936, respectively, after 10,000 epochs of training (Figure 3a); for the HKA site, the correlation coefficients for the training set and the validation set are approximately 0.9984 and 0.9933, respectively (Figure 3b); for the CCH site, the correlation coefficients of the training set and the validation set are approximately 0.9970 and 0.9833, respectively (Figure 3c); for the TKL site, the correlation coefficients of the training set and the validation set are approximately 0.9969 and 0.9926, respectively (Figure 3d). The high correlation coefficients between the outputs of the 1D-CNN filter and the Lanczos filter for both the training set and validation set indicate that the 1D-CNN filter can accurately extract QBWO and ISO signals at all of the four stations. This demonstrates that the 1D-CNN filter effectively replicates the results of the Lanczos filter, even though it employs a window length that is half of that of the Lanczos filter. Figure 3: The MSE losses (unit: \({}^{\circ}\)C; solid lines) and correlation coefficients (dashed lines) between the outputs of 1D-CNN filter and Lanczos filter during the training process (blue) and validation process (red). Results are based on the daily mean temperature observations of the (**a**) HKO, (**b**) HKA, (**c**) CCH, and (**d**) TKL stations. The validity of the 1D-CNN filtering approach is also evident for all of the other 10 stations employed in this study. We compare the results obtained with the 1D-CNN filter for time series data from the 14 stations between 2010 and 2020 with those obtained using Lanczos filtering. The calculated evaluation metrics, including the _MAE_, _MSE_, _RMSE_, and \(R^{2}\), are presented in Table 2. The _MAE_ values range from 0.053 to 0.066, with a mean value of 0.059. The MSE values range from 0.007 to 0.012, with a mean value of 0.009. The RMSE values range from 0.082 to 0.111, with a mean value of 0.097. The \(R^{2}\) values range from 0.995 to 0.998, with a mean value of 0.996. All these metrics indicate that the 1D-CNN filter is able to reproduce bandpass-filtered signals that are highly consistent with those generated by the Lanczos filter. The evaluation metrics for the 14 stations confirm that the results we obtained are not just cherry-picked examples. The outstanding performance of the 1D-CNN bandpass filter can be directly illustrated by comparing between the original time series, the time-filtered series processed with a Lanczos filter, and the time-filtered series processed with a 1D-CNN filter. Figure 4 gives a comparison of the HKO, HKA, CCH, and TKL stations in the year 2022.