# Improving PM2.5 Concentration Forecast with the Identification of Temperature Inversion
## 2 Literature Review
### PM\({}_{2.5}\) Forecasting  
The existing PM\({}_{2.5}\) forecasting approaches fall into three prevailing categories. (1) Regression or autoregression methods: The regression methods require explanatory variables in addition to the PM\({}_{2.5}\) series itself, while the autoregression methods need only the PM\({}_{2.5}\) series. Regression methods can be effective if the selected explanatory variables are informative and sufficient to describe the PM\({}_{2.5}\) concentrations. The widely used explanatory variables include wind speed and direction, precipitation, temperature, relative humidity, atmospheric pressure, land use, traffic amount, road types, satellite images, to name a few. The effectiveness of each explanatory variable depends on the climate ecology and anthropogenic activities in the studied location. Both linear [20, 21, 22] and nonlinear [23, 24, 25] regression models have been employed in the literature. Autoregression methods focus on discovering the temporal trends contained in the PM\({}_{2.5}\) time series. Autoregressive integrated moving average model (ARIMA) was adopted in [26] to explore the short-term time series and estimate the mean daily PM\({}_{2.5}\) concentration. Generalized autoregressive conditional heteroscedasticity (GARCH) model was used in [27] to capture linear and nonlinear panel information for PM\({}_{2.5}\) concentrations forecasting. (2) Machine learning methods: Among others, support vector machine (SVM) and artificial neural networks (ANN) are the most popular ones. [PERSON] et al. [28] constructed an SVM to forecast PM\({}_{2.5}\) concentrations in Bogota which is a tropical city with complex terrains. The SVM model is trained to represent the behavior of days with high PM\({}_{2.5}\) concentrations and those with fast changes in PM\({}_{2.5}\) tendency. An SVM was developed in [29] for PM\({}_{2.5}\) class prediction. Three most relevant meteorological variables are extracted by measuring the cosine similarity among records in the same PM\({}_{2.5}\) class. With the identified meteorological variables, the SVM is trained to make the classification. The training parameters of the  
Figure 1: Temperature inversion. (**a**) Normal aerosol convection; (**b**) inhibited aerosol convection under the warm air inversion layer.  
SVM are optimized by the particle swarm optimization (PSO) algorithm to improve the classification accuracy. A specific type of ANN named multiple layer perceptron (MLP) is adopted in [30] to learn the relationship between PM\({}_{2.5}\) concentration and a set of meteorological factors with satellite-derived AOD data. An ensemble model was established in [31] to combine PM\({}_{2.5}\) estimates from three machine-learning methods, namely, neural network, random forest, and gradient boosting. A deep-learning long short-term memory (LSTM) model was proposed in [32] for predicting daily PM\({}_{2.5}\) concentration in China. The spatiotemporal information of surrounding monitoring stations is used to adjust the prediction model. Another deep learning network consisting of a CNN and an LSTM was deployed in [33]. The CNN is designed to extract meteorological features from 14 sites in Shanghai and the LSTM is used to model time dependence of pollutants. (3) Hybrid methods. An increasing number of recent works developed hybrid approaches which boost the performance by complementing the strengths and weaknesses of individual models. In particular, regression has been hybridized with ANN [34] and SVM [27]. It is worth noting that most hybrid methods combine complementing models to build a stronger predictor. To the best of our knowledge, none has intended to combine contrasting machine-learning models in various phases such as meteorological pattern classification and PM\({}_{2.5}\) concentration prediction as we have in our paper.  
Different periods of training time span have been considered in the literature, ranging from a couple of days covering a pollution event, a monsoon season, an entire year, to a longer-term multiyear dataset [11; 12; 25;