## 4 Summary and Discussion  
In this study, a short-term PM\({}_{2.5}\) concentration prediction model is established based on four deep learning neural networks (namely, EEMD, BP, CNN and LSTM). The EEMD algorithm is designed to decompose the original PM\({}_{2.5}\) timeseries to high- to low-frequency IMFs. Each IMF component, along with meteorological variables, is trained and predicted by three other neural networks. The summation of all IMF prediction can be treated as the prediction for the original PM\({}_{2.5}\) concentration. To assess the model effectiveness, we designed four sensitivity experiments and compared their MAEs in five pollution levels. It is found that the performance of a hybrid model is generally better than a single model, which is consistent with most previous studies. Figure 5: Comparison of observed and predicted values for high-frequency modes (IMFs 1 and 2) and low-frequency modes (IMFs 3 to 8) with different models. (**a**) MAE and correlation coefficient for high-frequency modes (IMFs 1 and 2) for test 1; (**b**) MAE and correlation coefficient for high-frequency modes (IMFs 1 and 2) for test 2; (**c**) MAE and correlation coefficient for low-frequency modes (IMFs 3 to 8) for test 1; (**d**) MAE and correlation coefficient for low-frequency modes (IMFs 3 to 8) for test 2. Figure 6: MAE of different models under different pollution levels. To reduce the prediction errors, previous studies have investigated different combinations of neural networks to improve the structure of the prediction model [9; 21; 24; 32]. However, the prediction of the PM\({}_{2.5}\) concentration in heavily polluted seasons still remains a challenge. Different from all previous studies, we assumed that a PM\({}_{2.5}\) timeseries in winter seasons contains full timescale variability due to complexity of weather conditions, pollution sources and emissions, which makes it really challenging for any neural network to be trained based on a limited data set. Therefore, in this study the EEMD algorithm is first used to decompose the original PM\({}_{2.5}\) sequence to several IMFs from high to low frequencies. Each IMF component is trained and predicted by an individual neural network. The results showed that both BP and LSTM are able to fit very well the low-frequency IMFs. Although high-frequency IMF components remain a challenge due to some chaotic processes, the total prediction errors of the summation of all IMFs are remarkably reduced. The PM\({}_{2.5}\) concentration is obviously related to the surrounding area, notably Hebei province. To investigate the impact of spatial information on the PM\({}_{2.5}\) prediction in Beijing city, 143 stations in Northern China were used to construct a CNN-LSTM hybrid model. The results showed that, under extreme conditions of PM\({}_{2.5}<35\) and PM\({}_{2.5}>150\), the CNN-LSTM outperforms the single LSTM by \(\sim\)30%. This implies that a PM\({}_{2.5}\) timeseries has its own temporal and spatial variability. A well-designed hybrid model on the PM\({}_{2.5}\) intrinsic modes and characteristics can improve its prediction skills. Regarding the very high-frequency component (IMF-1), we found that its spectrum is very similar to white noise, which might be due to microphysical processes, such as turbulence and chaotic processes, that cannot be learned by a simple neural network model. This may provide us with a new topic for future research. Conceptualization and methodology, [PERSON]; software and validation, F.Y. ; formal analysis, investigation, data curation, X.-C.R., S.Z. ; writing--original draft preparation, [PERSON]; writing--review and editing, J.W. ; visualization, F.Y. ; supervision, J.W. ; project administration, J.W. ; funding acquisition, J.W. All authors have read and agreed to the published version of the manuscript.