Development of a CNN+LSTM Hybrid Neural Network for Daily PM_2.5 Prediction

Abstract

A CNN+LSTM (Convolutional Neural Network + Long Short-Term Memory) based deep hybrid neural network was established for the citywide daily PM_2.5 prediction in South Korea. The structural hyperparameters of the CNN+LSTM model were determined through comprehensive sensitivity tests. The input features were obtained from the ground observations and GFS forecast. The performance of CNN+LSTM was evaluated by comparison with PM_2.5 observations and with the 3-D CTM (three-dimensional chemistry transport model)-predicted PM_2.5. The newly developed hybrid model estimated more accurate ambient levels of PM_2.5 compared to the 3-D CTM. For example, the error and bias of the CNN+LSTM prediction were 1.51 and 6.46 times smaller than those by 3D-CTM simulation. In addition, based on IOA (Index of Agreement), the accuracy of CNN+LSTM prediction was 1.10–1.18 times higher than the 3-D CTM-based prediction. The importance of input features was indirectly investigated by sequential perturbing input variables. The most important meteorological and atmospheric environmental features were geopotential height and previous day PM_2.5. The obstacles of the current CNN+LSTM-based PM_2.5 prediction were also discussed. The promising result of this study indicates that DNN-based models can be utilized as an effective tool for air quality prediction.

1. Introduction

PM_2.5 (particulate matter with an aerodynamic diameter of ≤2.5 μm) is a very harmful air pollutant. Several epidemiological studies have evaluated the harmfulness of this pollutant [1,2]. In South Korea, PM_2.5 is one of the most concerning air pollutants. During the cold seasons, high PM_2.5 events frequently occur. To prevent public damage caused by high PM_2.5, the National Institute of Environmental Research (NIER) of South Korea has conducted air quality forecasts using a three-dimensional chemistry transport model (3-D CTM) based ensemble system since 2014.

However, the accuracy of current CTM-based air quality prediction is known to be relatively low for PM_2.5. The CTM estimations have several sources of uncertainty: emission inventories, meteorological fields, initial and boundary conditions, and physico-chemical mechanisms. Great efforts have been made to enhance the predictive performance of 3-D CTMs [3,4,5,6]. Nevertheless, it is not yet clear when the air quality predictions will be sufficiently accurate. Therefore, in order to estimate more accurate ambient levels of PM_2.5, it is necessary to develop a new model that makes predictions with a different operating principle from traditional CTMs.

Recently, artificial intelligence (AI) algorithms such as decision tree (DT)-based ensembles and deep neural networks have been utilized in air quality prediction [7,8,9,10,11,12,13,14,15,16,17,18,19]. For the optimal algorithm for PM_2.5 prediction, several previous studies have performed comprehensive performance comparisons between AI algorithms [7,8,9,10]. As shown in

Table 1. Performance comparison between AI-based PM_2.5 prediction models *.

References	Study Area	Period	Algorithm	RMSE (μg/m3)
Joharestani et al., 2019 [7]	Tehran, Iran	2015–2018	Random forest	14.47
			XGBoost	13.66
			MLP	15.11
Karimian et al., 2019 [8]	Tehran, Iran	2013–2016	MART	13.19
			DFFN	19.62
			LSTM	9.42
Li et al., 2020 [9]	Beijing, China	2010–2014	CNN+LSTM	17.93
			LSTM	18.08
Park et al., 2020 [10]	Beijing, China	2015–2017	MLP	37.79
			LSTM	11.34
			CNN+LSTM	5.357

* XGBoost stands for extreme gradient boosting; MLP stands for multi-layer perceptron; MART stands for multiple additive regression trees; DFFN stands for deep feed forward neural network.

, in general, it is well known that artificial neural network (ANN) algorithms tend to predict PM_2.5 more accurately than the DT-based ensemble algorithms. Because of the advantages of predictive performance, ANN algorithms have shown a wide range of applications in the field of air quality prediction. For example, general deep neural network (DNNs)-based air quality models have been established to estimate the ground levels of O₃ [11,12]. In addition, recurrent neural networks (RNNs), an ANN specialized in time-series prediction, have been used in PM_2.5 predictions [13,14,15,16]. Moreover, convolutional neural network (CNN)-based DNNs have been developed to estimate ambient levels of air pollutants by considering the spatial distribution of meteorological and atmospheric environmental variables together [17,18,19]. Unlike the traditional CTMs, these ANNs make predictions in a data-driven manner (i.e., without consideration of sophisticated atmospheric processes). Because of their operation principles, ANN-based prediction is known to be more cost-effective than the CTM-based estimation. In this study, for more accurate daily PM_2.5 prediction, a CNN+LSTM hybrid model was established.

ANNs have their own specialized functions depending on the type or structure. For example, RNNs have a unique structure that allows past experiences to be stored in their internal pinholes (or memory cells). Because of this capability, RNNs have shown superior performance in time-series prediction [20,21]. In particular, among the RNNs, long short-term memory (LSTM) cells have shown a wide range of applications because of their low probability of gradient exploding and vanishing [22,23,24]. In addition, CNN is the most specialized ANN for finding the latent information in multi-dimensional data (e.g., language, voice, and image). To analyze multi-dimensional data, general DNNs require the construction of hidden nodes with extremely complex and deep structures. In contrast, CNNs can significantly reduce computation costs by sharing the convolutional kernels (or filters), and this type of ANN has also shown superior analytical capabilities for high-dimensional datasets compared to other ANNs [25,26,27]. For accuracy improvement of air quality prediction, recent studies have proposed the development of hybrid DNNs utilizing both special functions of CNN and LSTM [9,10,19].

It is well known that the concentration of PM_2.5 in South Korea is under the great influence of domestic and international emission sources [28]. The East Asian atmospheric pressure pattern determines the degree of the said influences. For example, in stagnant conditions, PM_2.5 emitted from domestic sources accumulates, and the concentration of PM_2.5 increases. In addition, if the intensity of the westerly wind increases, air pollutants originating from China move to South Korea and the ambient levels follow suit—the levels increase. Therefore, for more accurate DNN-based PM_2.5 prediction, it is necessary to utilize ANNs that can effectively analyze atmospheric pressure patterns over East Asia. Furthermore, the possibility of gradient exploding and vanishing caused by using a long-term training dataset should be minimized. For these reasons, we propose a CNN+LSTM hybrid system for daily PM_2.5 prediction.

In this study, the CNN+LSTM model was optimized through comprehensive sensitivity tests. The details of the model development are described in Section 2. This section also provides detailed information on the configuration of the input features and the structure of the CNN+LSTM. Evaluation of the newly developed hybrid system is conducted through the comparisons between the CNN+LSTM-based predictions, the observations, and 3-D CTM estimations in Section 3. The discussions of the advantages and limitations of the current CNN+LSTM model are in Section 4.

2. Model Development

2.1. Dataset

We constructed 3.1-year big data for model development (May 2017 to December 2019) and prediction (November 2016 to April 2017). In this study, the data produced after 2019 were not included in the construction of the big data because of COVID-19 (coronavirus disease 2019)-induced anomalies in air quality patterns. As input variables, NCEP (National Center for Environmental Prediction) GFS (Global Forecast System) forecast, KMA (Korea Meteorological Administration), ASOS (Automated Surface Observing System) observations, and NIER AIR KOREA observations were obtained from their official websites (https://rda.ucar.edu/datasets/ds084.1/, last accessed: 11 November 2022; https://rda.ucar.edu/datasets/ds084.1/, last accessed: 11 November 2022; https://www.airkorea.or.kr/web/, last accessed: 11 November 2022). In order to represent the pressure pattern over East Asia, the latitudinal and longitudinal boundaries of GFS were set from 20° N to 52° N and 96° E to 144° E. The forecast product of GFS has a resolution of 0.25° × 0.25°, respectively (i.e., the dimension of the GFS forecast was 128 × 192). Since the time interval of the GFS forecast is three hours, we performed linear interpolation to estimate the hourly forecast dataset.

Figure 1 presents locational information of ASOS and AIR KOREA ground monitoring stations, which consist of 103 and 494 monitoring sites throughout South Korea, respectively. ASOS network provides hourly observed meteorological variables, and the AIR KOREA network provides hourly concentrations of air pollutants (refer to

Table 2. Input variables of CNN+LSTM hybrid PM_2.5 prediction model.

Data Type	Variable	Unit	Time Resolution	Feature Type
Observed meteorological variable	Temperature	K	1 h	Temporal feature
	Wind speed	m/s
	Wind direction	°
	Relative humidity	%
	Vapor pressure	hPa
	Dew point	K
	Pressure	hPa
	Sea level pressure	hPa
Observed atmospheric environmental variable	SO2	ppmv	1 h	Temporal feature
	CO	ppmv
	O3	ppmv
	NO2	ppmv
	PM10	μg/m3
	PM2.5	μg/m3
Predicted meteorological variable	Geopotential height *	gpm	3 h	Spatial feature

* Geopotential height at 850 hpa.

). Among the monitoring sites, the urban observation sites located in seven major cities (with a population of more than one million) in South Korea were selected for daily PM_2.5 predictions (refer to Figure 1a–g). For the prediction of citywide PM_2.5, the observations of the selected sites located in each city were averaged. Table 2 is the detailed information on input variables.

Similar to this study, several previous studies have proposed the use of the integration of input features of both observation-based meteorological and air quality information for more accurate DNN-based PM_2.5 predictions [13,29]. The selected input variables are closely related to the concentrations of PM_2.5. For example, wind speed and amount of precipitation can directly represent the intensity of atmospheric turbulent dispersions and wet scavenging processes, and the concentrations of primary pollutants such as CO and SO₂ can denote the degree of domestic anthropogenic emissions. In addition, combining input features allows DNN-based models to consider more diverse atmospheric environmental properties. Among the meteorological variables, wind speed, wind direction, pressure, and geopotential height can represent the possibility of long-range transport of air pollutants. Moreover, by co-considering meteorological and air quality variables such as O₃, NO₂, temperature, and relative humidity, the intensity of atmospheric oxidation processes can be reflected in the DNN-based prediction.

The input variables were normalized before feeding into the CNN+LSTM hybrid model to prevent overestimating the effect of the variables with large-scale values.

$$x_{normal, i}=\frac{x_i-x_{min,i}}{x_{max,i}-x_{min,i}}$$

(1)

here $x_{normal, i}$ is the normalized value of variable i; $x_i$ is the value of variable i; $x_{max,i}$ and $x_{min,i}$ are maximum and minimum values of variable i, respectively. The previous day’s observations and the next day’s geopotential height forecasts were normalized and merged with the next day’s PM_2.5-observations.

2.2. Model Construction

The procedure of the CNN+LSTM-based daily PM_2.5 prediction is summarized in Figure 2. The proposed model consists of three parts: i) feature representation, ii) data vector fusion, and iii) PM_2.5 prediction. As shown in the figure, we extracted the spatial feature of the GFS forecast and temporal features of ground observations in the feature representation step. In order to represent the spatial latent features, two CNN layers were embedded. Comprehensive sensitivity tests have been made to determine the number and structure of deep hidden layers. For example, CNN-based autoencoders have been constructed en masse. We elected the type of CNN layers and their structural hyperparameters (the size and number of convolutional filters) based on the reproduction accuracy of the constructed autoencoders. Based on the result, we decided to embed two three-dimensional CNN (3-D CNN) layers to represent the spatial features. The kernel size of CNN layers was set to 3 × 3 × 3. The number of kernels for the first and second CNN layers were 32 and 24. The input dimension of the first 3-D CNN layer was set to 24 × 128 × 192 × 1 for daily PM_2.5 prediction. We embedded two 3-D max pooling layers for downscaling the vector matrices extracted from the CNN layers. The pooling size was set to 2 × 2 × 2.

Latent features extracted through convolutional operations were subjected to the next flatten and LSTM layers for data fusion with temporal features. We injected observation-based input features (i.e., ASOS and AIR KOREA observations) into two LSTM-based hidden layers to extract the characteristic of temporal input features. The input dimension of the first LSTM layer was 24 × 14. Additionally, we determined the number of hidden nodes of the entire LSTM layers through sensitive tests. The number of the LSTM hidden nodes was 512. In the second step, the vectors of temporal and spatial latent information extracted through the first step were fused as they passed the concatenate layer. Since the number of LSTM hidden nodes was set to 512, the concatenate layer generates 1024 output vectors. The concatenate layer was connected to the final dense layer. This dense layer identifies the relationship between the outputs of concatenate layer and the true values (observed PM_2.5).

Table 3. Configuration of the CNN+LSTM hybrid neural network model.

Prediction Step	Structural Hyperparameter	Neural Network
		1st CNN	1st Max Polling	2nd CNN	2nd Max Polling	Flatten	LSTM
Feature representation for spatial features	Input shape	(None, 24, 128, 192, 1)	(None, 24, 128, 192, 32)	(None, 12, 64, 96, 32)	(None, 12, 64, 96, 24)	(None, 6, 32, 48, 24)	(None, 221184)
	CNN kernels or hidden nodes	32	-	24	-	-	512
	Kernel size	(3, 3, 3)	-	(3, 3, 3)	-	-	-
	Activation	ReLU	-	ReLU	-	-	Tanh
	Pooling size	-	(2, 2, 2)	-	(2, 2, 2)	-	-
	Output shape	(None, 24, 128, 192, 32)	(None, 12, 64, 96, 32)	(None, 12, 64, 96, 24)	(None, 6, 32, 48, 24)	(None, 221184)	(None, 512)
Feature representation for temporal features		1st LSTM			2nd LSTM
	Input shape	(None, 24, 14)			(None, 24, 512)
	Hidden nodes	512			512
	Activation	Tanh			Tanh
	Output shape		(None, 24, 512)		(None, 512)
Data vector fusion		Concatenate layer
	Input shape	[(None, 512), (None, 512)]
	Output shape	(None, 1024)
PM2.5 prediction		Final dense layer
	Input shape	(None, 1024)
	Hidden nodes	24
	Activation	Leaky-ReLU
	Output shape	(None, 24)

shows the summary of detailed configuration information of the CNN+LSTM hybrid model.

To identify this complicated and non-linear relationship, we need to utilize an activation function for the final dense layer. There are several functions for the activation of DNNs. Among them, rectified linear unit (ReLU) is the most versatile because of its low computation cost [30]. As the output of ReLU ranges from 0 to ∞, its derivative is 0 or 1. Therefore, this function is free from the gradient vanishing and exploding during the back propagations. However, when the hidden node outputs a negative value, the gradient of ReLU is zero, and thus the learnable parameters (weights and biases) associated with the node cannot be adjusted or updated during the model training. In addition, if a huge number of hidden nodes output negative values, training loss can no longer be reduced (i.e., dying ReLU). To prevent the said problem, we used the leaky rectified linear unit (Leaky-ReLU) as the activation function [31]. The Leaky-ReLU expressed by

$$f\left(x\right)=\{\begin{array}{c}\alpha x when x<0\\ x when x\ge 0\end{array}$$

(2)

as shown in the equation, the derivative of Leaky-ReLU is $\alpha$ or 1. In this study, we set the value of $\alpha$ as 0.3.

2.3. CNN+LSTM Optimization

Model optimization is a process of finding the optimal combination of weight and bias matrices (learnable parameters). As mentioned previously, the structural hyperparameters of the CNN+LSTM model were determined from the massive amounts of sensitivity tests. There are two main components in DNN optimization: (i) cost function and (ii) optimizer. Their respective roles are to evaluate the accuracy of the updated learnable parameters and to discover efficient and/or stable reduction paths for the cost (or loss). Several cost functions have been utilized in the optimization of DNNs. For better predictive performance, it is very important to select an appropriate objective function corresponding to the purpose of the DNN model. Since the proposed hybrid model was the regression model, the mean squared error (MSE) was utilized as a cost function in this study. The MSE expressed as

$$J_{MSE}\left(\theta \right)=\frac{1}{N}{\displaystyle \sum }_{i=1}^N{\left(y_i-h_{\theta }\left(x_i\right)\right)}^2$$

(3)

here $y_i$ is the true value for $i$th training; $x_i$ is input for $i$th training; $h_{\theta }\left(x_i\right)$ is the predicted value by the given model $\theta$. In this study, adaptive moment estimation (ADAM) was used as an optimizer [32]. The ADAM is an extended stochastic gradient descent algorithm. This algorithm determines the individual adaptive learning rates for different learnable parameters by computing the first and second moments of their gradients.

To train the CNN+LSTM hybrid model, the 2.7-year data (May 2017 to December 2019) were used, as mentioned previously. We divided this dataset into two groups with ratios of 80% for model training and 20% for validation. To confirm the suitability of model optimization, the variations of MSE for model training and validation were monitored during the model training. In the early stage of model optimization, the MSEs of the training and validation decrease together by updating weights and biases. Because training data are only considered in the adjustment of weight and bias matrices, the training cost continuously decreases with the iterative update of learnable parameters. However, the validation MSE decreases until the specific update, and then it stagnates or starts to increase. The optimization of DNNs is to update the learnable parameters until this stagnant or inflection point [33]. If the DNN is properly optimized, the validation MSE at this point should be slightly higher than the training MSE. When the validation MSE is much higher than the training MSE, this represents that the learnable parameters are overturned (i.e., overfitting). On the contrary, if the training cost is bigger than the validation cost, it is called underfitting. From the perspective of improving the predictive performance and generalization of DNNs, it is crucial to minimize the possibility of overfitting and underfitting. To achieve this goal, iterative model training was performed, and then the models with the smallest gap between the training and validation cost were selected for daily PM_2.5 prediction. In addition, we also compared the training and validation MSEs and root mean squared errors (RMSEs) to re-evaluate the suitability of model training. The results of this evaluation are summarized in

Table 4. Evaluation of the suitability of model optimization *.

City	Training		Validation
	MSE	RMSE	MSE	RMSE
Seoul	131.85	11.48	152.81	12.36
Incheon	133.21	11.54	145.98	12.08
Daejeon	95.04	9.75	98.65	9.93
Gwangju	105.72	10.28	127.63	11.30
Daegu	87.57	9.36	96.20	9.81
Ulsan	101.60	10.08	112.51	10.61
Busan	124.09	11.14	140.84	11.87

* The units of MSE and RMSE are μg/m³.

. Based on this, we confirmed that the CNN+LSTM model was suitably trained.

2.4. 3-D CTM-Based PM_2.5 Prediction

We made the comparison between the CNN+LSTM-based PM_2.5 prediction and the CTM-predicted PM_2.5 to evaluate the predictive performance of the CNN+LSTM hybrid neural network model. In this study, we utilized the community multiscale air quality (CMAQ) model v5.2.1 for the 3-D CTM prediction. The meteorological fields for CMAQ prediction were estimated from weather research and forecasting (WRF) v3.8.1 model simulation. Figure 3 presents the boundary of the CMAQ prediction. As shown in the figure, the CMAQ boundary covers northeast Asia. The horizontal resolution of the CMAQ simulation was set to 15 × 15 km². The KORUS v5.0 emission inventory was used for anthropogenic emissions [34]. The biogenic emissions were acquired from the MEGAN (Model of Emissions of Gases and Aerosols from Nature) v2.1 simulation [35]. The emissions for biomass burning were acquired from FINN (Fire Inventory from National Center for Atmospheric Research, https://www.acom.ucar.edu/Data/fire/, last accesses: 11 November 2022) v1.5 [36]. The lateral boundary conditions were obtained from the official data archive of MOZART-4 (Model for Ozone and Related Chemical Tracers version 4, https://www2.acom.ucar.edu/gcm/mozart-4, last accessed: 11 November 2022), respectively [37].

2.5. Evaluation Metric

In this study, to evaluate the prediction performance of the CNN+LSTM and 3-D CTM, we introduced the following six scientific performance metrics, such as IOA (Index or Agreement), R (Pearson correlation coefficient), RMSE, MB (Mean Bias), MNGE (Mean Normalized Gross Error), and MNB (Mean Normalized Bias). These evaluation metrics were estimated as below:

$$\mathrm{IOA}=1-\frac{{{\displaystyle \sum }}_{i=1}^N{\left(C_{Model}-C_{Obs}\right)}^2}{{{\displaystyle \sum }}_{i=1}^N{\left(\left|C_{Model}-\overline{C_{Obs}}\right|+\left|C_{Obs}-\overline{C_{Obs}}\right|\right)}^2}$$

(4)

$$\mathrm{R}=\frac{{{\displaystyle \sum }}_{i=1}^N\left(C_{Model}-\overline{C_{Model}}\right)\left(C_{Obs}-\overline{C_{Obs}}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^N{\left(C_{Model}-\overline{C_{Model}}\right)}^2{{\displaystyle \sum }}_{i=1}^N{\left(C_{i,Obs}-\overline{C_{Obs}}\right)}^2}}$$

(5)

$$\mathrm{RMSE}=\sqrt{\frac{1}{N}{\displaystyle \sum }_{i=1}^N{\left(C_{Model}-C_{Obs}\right)}^2}$$

(6)

$$\mathrm{MB}=\frac{1}{N} {\displaystyle \sum }_{i=1}^N\left(C_{Model}-C_{Obs}\right)$$

(7)

$$\mathrm{MNGE}=\frac{1}{N} {\displaystyle \sum }_{i=1}^N\left(\frac{\left|C_{Model}-C_{Obs}\right|}{C_{Obs}}\right)\times 100$$

(8)

$$\mathrm{MNB}=\frac{1}{N} {\displaystyle \sum }_{i=1}^N\left(\frac{C_{Model}-C_{Obs}}{C_{Obs}}\right)\times 100$$

(9)

here $C_{Model}$ and $C_{Obs}$ represent the modeled and observed PM_2.5, $\overline{C_{Model}}$ and $\overline{C_{Obs}}$ are the averaged $C_{Model}$ and $C_{Obs}$.

3. Results

3.1. Model Evaluation

We performed the daily PM_2.5 prediction from November 2016 to April 2017. In order to evaluate the accuracy of the newly developed hybrid model, the CNN+LSTM-based PM_2.5 was compared to the observed PM_2.5. The CNN+LSTM-predicted PM_2.5 was also compared with that by CMAQ prediction. The results of this comparison are summarized in

Table 5. Scientific evaluations of the CMAQ- and CNN+LSTM-based PM_2.5 predictions *.

Model	City	Statistical Parameters
		IOA	R	RMSE	MB	MNGE	MNB
CMAQ	Seoul	0.70	0.52	19.70	−3.16	45.95	−6.10
	Incheon	0.70	0.53	19.46	−2.24	46.74	−1.63
	Daejeon	0.65	0.45	17.43	−1.30	49.80	3.98
	Gwangju	0.66	0.47	19.67	−6.15	50.68	−13.73
	Daegu	0.67	0.47	17.45	−5.80	45.26	−11.96
	Ulsan	0.67	0.49	17.01	−4.66	47.52	−10.34
	Busan	0.65	0.51	18.03	−9.70	48.34	−31.78
CNN+LSTM	Seoul	0.81	0.69	12.18	−0.84	35.89	12.39
	Incheon	0.82	0.68	12.55	−0.19	39.14	15.75
	Daejeon	0.73	0.58	11.22	−1.64	43.31	14.39
	Gwangju	0.72	0.55	14.66	−0.75	48.32	20.61
	Daegu	0.79	0.65	11.47	−1.27	39.92	11.44
	Ulsan	0.74	0.55	12.23	0.11	41.03	15.47
	Busan	0.73	0.58	10.96	−0.53	29.68	9.20

* The unit for RMSE and MB is μg/m³; the unit for MNGE and MNB is %.

and also shown in Figure 4. In the figure, the black-dashed line with an open circle represents the observed daily PM_2.5; blue-dashed and red lines represent the CMAQ- and CNN+LSTM-predicted daily PM_2.5; the grey shade represents the period with relatively high concentration among nationwide high PM_2.5 episodes, respectively. As shown in the figure, the CNN+LSTM predictions showed better agreements with the observations compared to the CMAQ-based predictions.

As shown in Figure 4 and Table 5, the CNN+LSTM predicted PM_2.5 more accurately than the CMAQ. The IOA for the CNN+LSTM-based PM_2.5 prediction ranged from 0.72 to 0.82. On the other hand, the CMAQ-based IOA ranged from 0.65 to 0.70. These differences in IOA demonstrate that the CNN+LSTM can produce 1.10–1.18 times better air quality information than the CMAQ. Based on the statistic metric, among seven cities, the CNN+LSTM predictions (0.81 ≤ IOA ≤ 0.82) at Seoul and Incheon showed the best agreements with the observations. The CMAQ-based predictions in these cities also showed better correlations with the observed PM_2.5 (IOA = 0.70). However, the accuracies of the CNN+LSTM at Daejeon, Gwangju, and Busan (0.72 ≤ IOA ≤ 0.73) were relatively low. The CMAQ predictions showed similar trends to the CNN+LSTM-based predictions (0.65 ≤ IOA ≤ 0.66).

In addition, the CNN+LSTM-based predictions showed fewer errors and lower biases. The RMSE for CNN+LSTM predictions ranged from 10.96 μg/m³ to 14.66 μg/m³, and those by CMAQ ranged from 17.01 μg/m³ to 19.70 μg/m³. The CNN+LSTM generated 1.51 times smaller deviation compared to the CMAQ. The prediction errors made by the CNN+LSTM showed significant improvement in Seoul and Busan; the improved rates in these cities were 38.17% and 39.21%. The CNN+LSTM-based predictions also showed lower biases than the CMAQ-based estimations. The MBs for the CMAQ predictions ranged from −9.70 μg/m³ to −1.30 μg/m³. These negative MBs indicate that the CMAQ model significantly underestimates ambient levels of PM_2.5. Although the CNN+LSTM-based predictions also showed negative biases (−1.64 μg/m³ ≤ MB ≤ 0.11 μg/m³), their values were 6.46 times smaller than those predicted by CMAQ.

As mentioned above, the PM_2.5 prediction was conducted from November 2016 to April 2017. During this cold season, high PM_2.5 events (PM_2.5 ≥ 40 μg/m³) occur frequently in South Korea. There were seventeen nationwide high PM_2.5 episodes. These high episodes are mainly attributable to the long-range transport of air pollutants by highly enhanced westerly wind and increased consumption of fossil fuels for domestic heating [22]. In particular, the daily PM_2.5 in Seoul increased up to 85 μg/m³ on January 1 and March 20, respectively. As shown in Figure 4, the CNN+LSTM model generated relatively high errors and biases during the nationwide high-PM events. Since DNNs optimize their weight and bias matrices in a data-driven manner, the corresponding errors and biases arise from the quality of the optimization dataset. Because DNNs are black box models, accurate investigation of data quality is practically impossible.

In this study, to indirectly present the data quality, we evaluated the data imbalance. The datasets used for the optimization of the CNN+LSTM model were highly imbalanced (i.e., the majority class of the training data consisted of the data samples with a relatively low concentration of PM_2.5). Since DNNs make predictions based on statistically generalized non-linear relationships between input features, it is difficult for the influence of minority-class data samples to be reflected in their estimations. The data samples with high PM_2.5 contributed just 11.30% on average. Among the seven training datasets, the training data for Seoul and Gwangju included the highest number of high-PM_2.5 incident samples; their contribution was 12.32% and 12.10%, respectively. In addition, Daejeon showed the lowest frequency of high-PM_2.5 incident samples (9.14%). However, as mentioned above, data imbalance is only an indirect indicator of data quality. Therefore, it is logically flawed to conclude that the cause of the performance degradation of the CNN+LSTM is entirely due to the said indicator.

3.2. Importance of Input Features

It is impossible to directly comprehend the relationship between input features and predictions of the DNNs due to the complex non-linearity between the outputs of the deeply structured hidden layers. In this study, we indirectly evaluated the influence of the input variables by sequential perturbing each feature. The main idea of this method is that: if the perturbed feature is “important” (i.e., an input feature has a larger influence on performance), the accuracy of the model predictions will be greatly reduced by the perturbation. In contrast, if the perturbed input feature is unnecessary, the predictive performance of the model will be rather improved. In this estimation, IOA was used as a basis for feature importance investigation because it can represent the overall accuracy of model prediction, as the statistical metric includes an error, bias, and correlation. The feature importance was estimated as below:

$$F{I}_i=\frac{({\mathrm{IOA}}_{w/o purtb}-{\mathrm{IOA}}_{i, purtb})}{{\mathrm{IOA}}_{w/o purtb}}\times 100$$

(10)

here $F{I}_i$ is the importance of feature $i$; ${\mathrm{IOA}}_{i, purtb}$ and ${\mathrm{IOA}}_{w/o purtb}$ are accuracies of the CNN+LSTM model with and without perturbation of feature $i$, respectively. The results of this estimation are summarized in

Table 6. Importance of the input features in daily PM_2.5 prediction *.

Type	Input Feature	Feature Importance
		Seoul	Incheon	Daejeon	Gwangju	Daegu	Ulsan	Busan
Meteorological variable	Geopotential height	25.29	22.00	21.86	36.41	7.92	15.04	14.32
	Temperature	12.87	12.54	9.82	9.71	4.70	3.10	5.95
	Wind speed	0.16	0.19	0.06	0.13	0.14	0.14	0.06
	Wind direction	1.86	3.90	0.30	2.22	2.71	1.29	0.48
	Relative humidity	1.86	1.84	7.40	7.88	3.65	7.79	3.65
	Vapor pressure	7.68	7.58	6.43	5.52	6.98	8.03	0.04
	Dew point	2.08	2.23	0.47	2.23	1.10	3.60	2.30
	Pressure	3.25	4.99	4.50	6.91	7.05	1.29	3.36
	Sea level pressure	2.60	2.37	2.61	7.26	7.29	2.56	3.00
Atmospheric environmental variable	SO2	2.67	1.87	1.86	6.22	7.93	2.91	2.36
	CO	1.74	0.92	0.28	3.69	1.38	1.96	0.40
	O3	8.06	3.33	10.44	15.73	6.79	8.87	3.66
	NO2	2.26	0.94	1.71	3.79	3.43	3.84	0.33
	PM10	0.96	1.64	5.08	0.77	1.20	2.36	4.58
	PM2.5	38.80	38.24	34.93	41.82	37.17	34.79	31.67

* The unit for feature importance is %.

.

As shown in Table 6, the importance of all input variables was positive. These positive values indicate that all input variables are necessary for daily PM_2.5 prediction (i.e., the appropriateness of variable selection). Among the atmospheric environmental variables, the previous day’s PM_2.5 and O₃ showed a great influence on the next day’s PM_2.5. Their importance ranged from 31.67% to 41.82% and from 3.33% to 15.73%, respectively. In particular, the previous-day-PM_2.5 was the most important input variable. Among the meteorological variables, PM_2.5 prediction was greatly influenced by geopotential height (from 7.92% to 25.29%) and temperature (from 3.10% to 12.87%). In particular, the importance of atmospheric pressure-related features was relatively higher compared to other meteorological variables. This result represents the importance of pressure patterns over East Asia and inside cities in the daily PM_2.5 prediction in South Korea. Therefore, the spatial and temporal pressure features should be included as the input variables in the construction of the DNN-based PM_2.5 model, and it is essential to embed CNN and LSTM together to extract their inherent information.

4. Conclusions

In this study, we developed a new CNN+LSTM hybrid neural network for daily PM_2.5 prediction. The performance of the CNN+LSTM model was precisely evaluated by comparing the CNN+LSTM-based PM_2.5 with the ground observations. In addition, the accuracy of the CNN+LSTM was compared with that of CMAQ to prove its usefulness as an air quality prediction tool. The CNN+LSTM hybrid model generated 1.51 and 6.46 times less error and lower bias on average than the CMAQ. In particular, based on IOA, the CNN+LSTM predictions were 1.10–1.18 times more accurate than the CMAQ estimations. This promising result clearly demonstrates that the DNN-based prediction model can be utilized as an effective tool for air quality prediction. In addition, a similar CNN+LSTM model can also be used in the prediction of other harmful air pollutants (e.g., NO₂, SO₂, and O₃).

In particular, the newly developed CNN+LSTM model is more cost-effective than the 3-D CTMs. Several pre-processing steps are required to generate a 3-D CTM-based air quality forecast: simulation of the numerical weather prediction model, preparation of biogenic and anthropogenic emission inventories, acquisition of initial and boundary conditions, and chemical speciation of air pollutants. Despite the efforts of these sophisticated pre-processings, the current 3-D CTM showed lower predictive power than the CNN+LSTM (refer to Section 3.1). On the other hand, the pre-processing of the CNN+LSTM-based prediction is very simple. For PM_2.5 predictions, it is only necessary to acquire the observational and forecast-based datasets from their official archives and configure input features. Nevertheless, the current CNN+LSTM model is superior to the 3-D CTM. Because of these advantages, for developing countries where it is impossible to establish and operate their own 3-D CTM-based forecast system due to financial limitations, the CNN+LSTM model developed through this study can be used as a more economical and efficient air quality forecast tool.

Although the current hybrid model can accurately predict PM_2.5, its performance can be deteriorated by two obstacles: i) the amount of available data and ii) an imbalance in training data. As shown in Section 3.1, the prediction accuracy of the CNN+LSTM model was very high for medium and relatively low concentrations (PM_2.5 < 40 μg/m³). In contrast, the CNN+LSTM tends to generate relatively high errors and biases for high PM_2.5 episodes. This inaccuracy originates from the amount and quality of the training data. The NIER of South Korea has officially conducted ground-based PM_2.5 monitoring since 2016. Although the PM_2.5 observations have been accumulated for seven years up to date, the amount of useful data for the CNN+LSTM development is less than four years, excluding the COVID-19 period. In addition, the data samples with high PM_2.5 only contributed 11.30% of the total available observations. Since DNNs statistically determine their predictions, it is very difficult to reflect the influence of these minority classes in the model estimation. In other words, from the perspective of the DNN generalization, the high PM_2.5 samples are likely to be recognized as noise signals during the model training. We believe that the current CNN+LSTM hybrid model can be more accurate by acquiring more data samples of minority classes through more observations.