Accurate multistep PM_{2.5} (particulate matter with diameters
With the rapid development of industrialization and economics, air pollution is becoming a serious environmental issue, which threatens humankinds’ health significantly. The PM_{2.5} concentration could reflect the air quality and has been widely applied for air quality management and control [
The current methods for PM_{2.5} forecasting could be divided into regressionbased, time seriesbased, and learningbased methods (also called datadriven methods) [
Learningbased methods, including shallow learning and deep learning, could extract the nonlinear relationships between meteorological variables and future PM_{2.5} concentrations that have been applied for PM_{2.5} forecasting. Support vector machine (SVM), one of the most attractive shallow learningbased methods, uses various nonlinear kernels to map the original meteorological factors into a higherdimension panel to improve forecasting accuracy. e.g., Deters et al. [
Deep learning technologies, including deep brief network (DBN), convolutional neural network (CNN) [
Year  Method  Data (Input)  Area  Forecasting type 

2017  DBN [ 
Seven meteorological data: maximum and minimum temperature, mean atmospheric pressure, mean relative humidity (RH), visibility.  Chongqing, China.  Daily singlestep 
2020  CNNBP [ 
Seventythree station data including air quality factors (PM_{2.5}, PM_{10,} SO_{2}, CO, O_{3}, NO_{2}), meteorological factors (temperature and RH).  Taiwan area  Hourly multistep 
2020  CNN [ 
The MODIS and GEOSChem AOD data, meteorological data, landuse variables, and regional and temporal dummy variables.  48 adjoining states and Washington DC, USA  Daily singlestep 
2020  GRU+ RNN [ 
Meteorological and air quality parameters (PM_{2.5}, PM_{10,} SO_{2}, CO, O_{3}, NO_{2}, etc.).  Turkey  Hourly singlestep 
2021  BiLSTM [ 
Historical PM_{2.5} series.  Beijing, China  Hourly singlestep 
2019  CNNLSTM [ 
Wind speed, wind direction, temperature from seven weather stations, historical PM_{2.5}, and air quality factors.  Shanghai, China  Hourly singlestep 
2019  GCLSTM [ 
Air quality factors, meteorological and time variables.  JingJinJi (Beijing, Tianjin and Hebei), China  Hourly singlestep 
2019  MICNNLSTM 
Air quality and meteorological data.  Beijing, China  Daily singlestep 
Although the above deep learningbased methods achieved good performance,
To our best of understanding, we are the first to make multisite multistep PM_{2.5} forecasting with the spacesharing mechanism only using the selfhistorical PM_{2.5} series.
A novel framework named SCNNLSTM with a multioutput strategy is proposed to forecast dailyahead multisite and multistep PM_{2.5} concentrations only using selfhistorical PM_{2.5} series and running once. Sufficient comparative analysis has confirmed its effectiveness and robustness in multiple evaluation metrics, including RMSE, MAE, MAPE, and R^{2}.
The effectiveness of each part in the proposed method has been analyzed.
The rest of the paper is arranged as follows. Section 2 gives a detailed description of the proposed SCNNLSTM. The experimental verification is carried out in Section 3. Section 4 discusses the effectiveness of the proposed SCNNLSTM for dailyahead multistep PM_{2.5} concentrations forecasting. The conclusion is conducted in Section 5.
Assume that we collected a long PM_{2.5} concentration series, denoted as
The current methods for multistep forecasting consist of direct and recursive strategies [
To avoid the above shortcomings, the proposed SCNNLSTM method adopted a multioutput strategy for multistep PM_{2.5} forecasting, as shown in
The proposed SCNNLSTM for multisite dailyahead multistep PM_{2.5} concentration forecasting consists of four steps: input construction, feature extraction, multispace feature sharing, output and update the network, as shown in
The proposed method adopted near
Due to the excellent feature extraction ability of CNN and the ability of LSTM to process time series with longtime dependency [
The space information is vital for PM_{2.5} forecasting as one space PM_{2.5} concentration is affected by adjacent spaces such as weather, environmental statues. To make full use of space information, the proposed method merged extracted
The fusion features are utilized to forecast future
To validate the proposed method's effectiveness, the authors implement the proposed SCNNLSTM based on the operating system of ubuntu 16.04.03, TensorFlow backend Keras. Moreover, the proposed method adopted “Adam” as the optimizer to find the best convergence path and “ReLu” as the activation function except the output layer is “linear.”
The authors adopted four realword PM_{2.5} concentration data sets to validate the proposed method's effectiveness, including Jongnogu, Junggu, Yongsangu, and Guangdonggu from Seoul, South Korea, which is available on the website of
Data  Length  Missing values  Maximum PM_{2.5} ( 
Minimum 
Samples 

Jongnogu  26, 280  816  148  1  1,095 
Junggu  26, 280  554  149  1  1,095 
Yongsangu  26, 280  1,003  173  1  1,095 
Guangdonggu  26, 280  872  205  1  1,095 
We utilized multiple metrics including root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and R square (R^{2}) to evaluate the proposed method from multiviews. The calculation of each metric is given in
The workflow for multisite and multistep PM_{2.5} concentration forecasting using the proposed SCNNLSTM, as shown in
To validate the effectiveness and priority of the proposed method for dailyahead multistep PM_{2.5} concentration forecasting, we compared the proposed SCNNLSTM with some leading deep learning methods, including CNN [
Methods  Structure #Layer (Neurons)  Activation function  Loss 

CNN [ 
InputConv1D(100, 3, 1)Conv1D(100, 3, 1)Conv1D(100, 3, 1)Output  ReLU  MSE 
LSTM [ 
LSTM(50)LSTM(50)output  ReLU  MSE 
CNNLSTM [ 
Authors’ code from 
To explore and verify the effectiveness of the proposed method for eachstep PM_{2.5} forecasting, we calculated averaged RMSE, MAE, MAPE, and R^{2} for each step on four sites using the above deep models except CNN as its MAPE does not make sense. The comparison results showed that the proposed method has an absolute advantage for each step forecasting on all evaluation metrics, which could be conducted from
Site
Method
RMSE
MAE
MAPE (%)
R^{2}
Jongnogu
CNN [
8.97 ± 2.00
6.84 ± 1.51
27.81 ± 4.47
0.70 ± 0.14
LSTM [
7.71 ± 2.05
5.34 ± 1.54
22.92 ± 5.64
CNNLSTM [
7.39 ± 1.86
4.74 ± 1.39
23.56 ± 3.32
0.70 ± 0.11
Proposed
0.73 ± 0.18
Junggu
CNN [
10.16 ± 6.57
6.96 ± 5.28

0.59 ± 0.29
LSTM [
7.96 ± 2.40
25.87 ± 6.60
0.63 ± 0.26
CNNLSTM [
7.84 ± 2.14
5.13 ± 1.64
23.40 ± 6.63
0.65 ± 0.21
Proposed
YongSangu
CNN [
20.37 ± 10.81
14.45 ± 8.35

0.32 ± 0.34
LSTM [
9.89 ± 1.97
6.35 ± 1.27
35.56 ± 6.46
0.50 ± 0.26
CNNLSTM [
8.76 ± 2.18
5.64 ± 1.67
26.82 ± 6.53
Proposed
0.71 ± 0.18
GangDonggu
CNN [
15.29 ± 10.04
10.72 ± 7.96

0.44 ± 0.24
LSTM [
5.80 ± 1.49
24.71 ± 6.60
0.67 ± 0.13
CNNLSTM [
9.62 ± 1.70
6.11 ± 1.37
26.23 ± 6.43
0.62 ± 0.14
Proposed
9.22 ± 1.79
Average
CNN [
13.70 ± 5.23
9.74 ± 3.62

0.51 ± 0.17
LSTM [
8.68 ± 1.03
5.55 ± 0.57
27.27 ± 5.66
0.64 ± 0.10
CNNLSTM [
8.40 ± 0.99
5.41 ± 0.60
25.00 ± 1.78
0.68 ± 0.05
Proposed
To explore each part's effectiveness in the proposed SCNNLSTM, we designed four subexperiments. Specially, designed spaceshared CNN (SCNN) to verify the effectiveness of LSTM; Designed spaceshared LSTM to verify the effectiveness of CNN; and designed CNNLSTM without a spaceshared mechanism (CNNLSTM alone) to verify its effectiveness; designed SCNNLSTM with a recursive strategy to validate the effectiveness of the multioutput strategy. All configurations of those methods are the same as the proposed method. The results based on subset 2 (Junggu), as shown in
The results indicated that the utilization of LSTM had improved RMSE by 5.97%, MAE by 6.74%, MAPE by 32.57%, and R^{2} by 1.49%, which conducts by comparing SCNN and the proposed method. The application of CNN has improved 5.14% of RMSE, 8.51% of MAE, 7.37% of MAPE, and 10.29% of R^{2}. By comparing the CNNLSTM alone with the proposed method, we can conduct that the spaceshared mechanism has improved 2.45% of RMSE, 2.02% of MAE, 3.18% of MAPE, and 1.49% of R^{2}. Moreover, by comparing the SCNNLSTM with a recursive strategy to the proposed method, the findings derived that the multioutput strategy has absolute priorities as it performs much better on RMSE, MAE, and MAPE except for R^{2} is a little worse. In summary, the above evidence proved that CNN could extract the shorttime gap feature; LSTM could mine hidden features which have a longtime dependency; The spaceshared mechanism ensures full utilization of space information; The multioutput strategy could save training cost simultaneously keeping high forecasting accuracy. Combining those parts properly could accurately forecast the multisite and multistep PM_{2.5} concentrations only using selfhistorical series and running once.
We have proposed a novel SCNNLSTM deep model to extract the rich hidden features from multisite selfhistorical PM_{2.5} concentration series for multisite dailyahead multistep PM_{2.5} concentration forecasting, as shown in
Method  RMSE  MAE  MAPE  R^{2} 

SCNN  8.04 ± 2.19  5.19 ± 1.51  33.37 ± 17.98  0.67 ± 2.20 
SLSTM  7.97 ± 2.11  5.29 ± 1.54  24.29 ± 6.04  0.61 ± 0.26 
CNNLSTM alone  7.75 ± 2.20  4.94 ± 1.61  23.24 ± 6.81  0.67 ± 0.21 
SCNNLSTM (recursive)  10.97 ± 4.91  8.10 ± 3.76  29.99 ± 1.07  
Proposed  0.68 ± 0.20 
To validate the proposed method's effectiveness, we compared it with three leading deep learning methods, including CNN, LSTM, and CNNLSTM, on four realword PM_{2.5} data sets from Seoul, South Korea. The comparative results indicated that the proposed SCNNLSTM outperforms others in terms of averaged RMSE, MAE, MAPE, and R^{2}, which could be conducted from
Moreover, the authors have explored the proposed method's effectiveness for eachstep forecasting, as shown in
To validate each component's effectiveness, an ablation study is done, as described in
By setting the parameters of the proposed SCNNLSTM, the forecasting accuracy could improve. Future studies will focus on using deep reinforcement learning technology to find the best parameter under the structure of the proposed SCNNLSTM.
This manuscript has developed an accurate, convenient framework based on CNN and LSTM for multisite dailyahead multistep PM_{2.5} concentration forecasting. In which, CNN is used to extract the shorttime gap features; CNN extracted hidden features are fed into LSTM to mine hidden patterns with a longtime dependency; Each site's hidden features extracted from CNNLSTM are merged as the final features for future multistep PM_{2.5} concentration forecasting. Moreover, the spaceshared mechanism is implemented by multiloss functions to achieve space information sharing. Thus, the final features are the fusion of shorttime gap, longtime dependency, and space information, which is the key to ensure accurate forecasting. Besides, the usage of the multioutput strategy could save training costs simultaneously keep high forecasting accuracy. The sufficient experiments have confirmed its stateoftheart performance. In summary, the proposed SCNNLSTM could forecast multisite dailyahead multistep PM_{2.5} concentrations only by using selfhistorical series and running once.