## 3 Methodology
### Data and Preprocessing  
The dataset contains meteorological parameters, measured values of pollutants' concentration from ground base stations, and predictive values of four pollutants predicted by the CMAQ model in South Korea from 1 January 2016 to 31 December 2016 recorded on hourly basis. Six ground-based pollutants observation are collected: PM\({}_{2.5}\), PM\({}_{10}\), sulfur dioxide, ozone, nitrogen dioxide, and carbon monoxide concentrations measured in \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\). They are available at Air-Korea website [32]. Six meteorological parameters (temperature, wind speed, relative humidity, surface roughness, planetary boundary layer, and precipitation) were taken from Korean public data website [33]. PM\({}_{2.5}\) has a strong correlation with the pollutants such as elemental carbon, nitrate, and ammonium, as described in various studies [34; 35], and ground-based sites do not measure these dependent pollutants, but CMAQ model has the ability to predict these features. CMAQ data have been predicted and provided by Air Lab at Gwangju Institute of Science and Technology [36] for the same time duration. The CMAQ model predictive features labels are: CMAQ_EC, CMAQ_ANO3, CMAQ_ANH4, and CMAQ_OTHR, measured in \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\). To check the models' performance, we selected data from four sites of Seoul and four locations of Gwangju (a city located south of Seoul). The average evaluation results from all the stations for each model with and without using CMAQ data are given in Section 4, which show that by including CMAQ features, we can get better prediction results. It is necessary to analyze the relationship between PM\({}_{2.5}\) and other features. For this purpose, a heat map is provided in Figure 2. The variables having the higher correlation with PM\({}_{2.5}\) concentrations are shown in dark red color while variables with less correlation are shown in light pink shade. The correlation of PM\({}_{2.5}\) with the pollutants from higher to lower is: PM\({}_{10}\) > ammonium = nitrate ions > carbon monoxide > other-pollutants > nitrogen dioxide > elemental carbon > sulfur dioxide. Ozone and other meteorological parameters are negatively correlated with PM\({}_{2.5}\) concentration. The order of negatively correlated features with PM\({}_{2.5}\) from highest to lowest are: relative humidity > surface roughness > precipitation > wind speed > ozone > planetary boundary level > temperature. To find data distribution of each feature, we used the histogram shown in Figure 3. There are 8727 records of data for each station, from which 7680 records were selected for training and 1023 used for testing the models (9:1 ratio for train and test dataset). The missing values were imputed by linear interpolation; data records from 1 January 2016 to 15 November 2016 were used for training and from 16 November to 31 December for testing the models. The inputs of the models are hourly observations of 16 selected features discussed above over the last 24 h and the output or label variable is the PM\({}_{2.5}\) concentrations that is the forecast for the next 1 h. The time duration for train and test datasets are separate from each other and do not overlap. For each prediction model, all the training was done on train dataset while validation and evaluation were made on test dataset. We used two gradient tree boosting machine learning models, namely extreme gradient boosting (XGBoost) and Light Gradient Boosting Machine (LightGBM), and reshaped the data to be appropriate for time series forecasting. Four very famous and ubiquitous deep learning models-Long Short-Term Memory (LSTM), a combination of Bidirectional and Unidirectional LSTM (BiULSTM), Gated Recurrent Unit (GRU), and Convolution LSTM (CNNLSTM)--were used. The results were compared after calculating their respective Mean Absolute Error (_MAE_), Root Mean Square Error (_RMSE_), Correlation Coefficient (_R_), and Index of Agreement (_IA_), which are given in Section 3.4.