# A Spatial-Temporal Approach for Air Quality Forecast in Urban Areas
## 3 Proposed Method
### Utilized Features  
Features that may affect PM2.5 were included for the PM2.5 forecast. A great deal of research has mentioned that meteorology data are highly related to PM2.5 [2; 3; 6; 9; 10; 13; 31; 32; 34; 36; 37; 39]. For example, when it is not rainy, the PM2.5 value increases as the relative humidity increases. However, the PM2.5 value usually drops rapidly when it starts to rain. In addition, as wind speed increases, air quality improves; air quality is better when a sea breeze is blowing, which usually carries particulate matter into the land breeze. This  
Figure 2: Framework of the spatial-temporal PM2.5 forecast approach. research also found meteorology data and air quality connections. Temperature, relative humidity, pressure, wind direction, wind speed, and daily rainfall were included in the meteorological data. In addition to meteorological data, the PM2.5 values had a lot to do with the spatial data. When a device monitored a good PM2.5 value, adjacent devices also monitored good values. In this study, the impacts of the atmosphere, regardless of individual factors, such as traffic emissions and factory emissions, were emphasized. These factors may have applied to time; for example, they are usually blocked during peak hours, or a factory emits exhaust gas at midnight. In this section, we will present the data used in the study. The dataset consists of temporal and spatial data. The features, types, and descriptions are introduced in Table 1.  
In this section, the method of PM2.5 forecasting is introduced. This study is dedicated to forecasting PM2.5 values over 48 h. Many studies have shown that meteorological data have a lot to do with air quality. We also found this connection in the data. Figure 3 shows the relationship between each feature difference and the PM2.5 value difference; it shows that, when a feature difference is smaller, the PM2.5 value difference is smaller. In terms of distance difference, the highest density was not close to zero. This was because the distance average of the data was about 6 km (Figure 3h), and data less than 6 km were not enough. Figure 3i concerns weather difference and PM2.5 difference. The weather difference (\(WD(t_{u},t_{v})\)) between times \(t_{u}\) and \(t_{v}\) was evaluated using Equation (1). There are \(m\) weather features in total. Each feature was normalized to 0-1 individually, and were compared with each observation from each time. The notation \(f_{k}(t)\) means the \(k\)-th weather feature at time \(t_{u}\). In Equation (1), it is assumed that the weight of each feature has the same value. The last figure shows that the PM2.5 value was probably similar when the weather showed high similarity. Therefore, a PM2.5 value forecast approach based on weather differences between the reference data and the target was designed. \[WD(t_{u},t_{v})=\sqrt{\sum_{k=1}^{m}[f_{k}(t_{u})-f_{k}(t_{v})]^{2}} \tag{1}\]  
PM2.5 data and weather data were combined for forecasting. The method is divided into temporal and spatial parts; in the temporal part, we used the weather and forecast weather data to estimate preliminary PM2.5 with a weighted-average formula. The weight depended on weather similarity. The data that were monitored over close periods of time, and which have a high weather similarity, were selected as references for the forecast. In the spatial part, it was found that the PM2.5 time series of adjacent devices during the same period was very similar. Figure 4 shows the PM2.5 time series for adjacent devices within 5 km. We can see that the PM2.5 time series of different devices were almost the same. Therefore, we used nearby monitoring stations to adjust the estimated value of PM2.5.