Development of a Prediction Model for Daily PM_2.5 in Republic of Korea by Using an Artificial Neutral Network

Abstract

This study aims to develop PM_2.5 prediction models using air pollutant data (PM₁₀, NO₂, SO₂, O₃, CO, and PM_2.5) and meteorological data (temperature, humidity, wind speed, atmospheric pressure, precipitation, and snowfall) measured in South Korea from 2015 to 2019. Two prediction models were developed using an artificial neural network (ANN): a nationwide (NW) model and administrative districts (AD) model. To develop the prediction models, the independent variables daily averages and variances of air pollutant data and meteorological data (independent variables) were used as independent variables, and daily average PM_2.5 concentration set as a dependent variable. First, the correlations between independent and dependent variables were analyzed. Second, prediction models were developed using an ANN to predict next-day PM_2.5 daily average concentration, both NW and in 16 AD. The ANN models were optimized using a factorial design to determine the hidden layer layout and threshold, and a seasonal (monthly) factor was also considered. In the optimal prediction model, the absolute error in 1 σ was 91% (in-sample 91%, out-of-sample 91%) for the NW model, and the absolute error in 1 σ was 86% (in-sample 88%, out-of-sample 84%) for AD model. The accuracy of these prediction models increases further when they are developed using the next-day weather data, assuming that the weather prediction is accurate.

1. Introduction

Particulate matter (PM) is a global concern that is emitted locally and moves intercontinentally via long-range transport [1,2]. PM_2.5 (particulate matter with an aerodynamic diameter smaller than 2.5 μm) can penetrate deep into the lungs and enter the bloodstream [3,4], which majorly affects the cardiovascular and respiratory systems [5] but also affects other organs. Exposure to air pollutants, including PM_2.5, reportedly causes 7 million premature deaths every year [6], and can cause lung function decline [7,8], respiratory infections [9,10], and asthma [11,12] in vulnerable groups, such as children. In developing countries, air quality improvement is urgently required because of the unprotected use of fossil fuels [13,14]. In 2013, the International Agency for Research on Cancer (IARC) classified outdoor air pollution and PM_2.5t as carcinogens [15]. In addition, in September 2021, the World Health Organization (WHO) lowered the new air quality guideline for PM_2.5 to an annual average of 5 μg/m³ from 10 μg/m³, considering the effects of the particles on the human body due to long-term exposure [16]. An accurate PM_2.5 daily prediction model help people plan their outdoor activities according to PM_2.5. It will contribute to reducing the incidence of diseases caused by PM2.5 concentration. Therefore, a PM_2.5 daily prediction model is developed in this study.

PM_2.5 is mainly emitted directly by fuel combustion in various sectors including transportation, energy, household, industry, and agriculture [17,18]. It is also emitted in the form of nitrogen oxide (NOx) or sulfur oxide (SOx) during the gas phase reaction with ammonia (NH₃) [19]. It is very difficult to control because it generates ammonium nitrate and ammonium sulfate, which are secondary PMs. Korea grapples with the effects of long-range transport as well as domestic emissions [20]. Although the concentration of PM_2.5 in Korea is decreasing, remarkable long-lasting pollution episodes often occur, but remain difficult to predict. The National Institute of Environmental Research has been using a community multiscale air quality (CMAQ) model to predict the concentration of PM_2.5 for air quality forecasting [21,22]. In the CMAQ model, meteorological and emission information are used as input data, although the accuracy of domestic and foreign emission information requires further improvement [23]. Korea forecasts PM_2.5 by classifying it into four stages (low, moderate, high, and very high), and in 2018, the accuracy of the one-day and two-day forecasts were 73% and 68%, respectively; thus, uncertainty regarding these forecasts remains [24].

In recent years, air pollution prediction studies using artificial neural networks (ANN) have been widely conducted to improve the uncertainty of air quality prediction [25,26]. ANNs are used to accurately predict pollutant concentrations because they can build complex nonlinear models [27,28,29,30]. Various studies have been undertaken to predict dust concentrations. A study was conducted to forecast PM2.5 concentration by building a prediction model based on the radial basis function (RBF) neural network and comparing it with the existing back propagation (BP) network model [31]. Another study used particle swarm optimization (PSO) and fuzzy neural network as a more optimized method to predict PM2.5 concentration using meteorological factors and chemical composition of PM2.5. A case in which ANN technology was successfully applied to predict the concentration of PM2.5 in the air in a complex road traffic network was used to predict the concentration at a specific point [32]. To compensate for the disadvantages of CMAQ, Chang-hoi et al. conducted a study that grafted a recurrent neural network (RNN) to CMAQ [24,33]. However, most existing studies optimize the model or predict the concentration in a specific situation.

McKendry (2002) predicted next-day PM_2.5 using ANN with today air pollutants’ (NOx, PM₁₀, PM_2.5, O₃) concentrations and their variances and next-day precipitation and temperature as input variables [34]. Sun and Sun (2017) developed hybrid model next-day PM2.5 using PCA, LSSVM, and Cuckoo search [35]. The model developed in this study shows improved predictive performance compared to the models of the previous two studies and is presented in the results and discussion section. Among various ANN models, the multilayer perceptron artificial neural network in this study is a feedforward type ANN model that can be used universally, unlike the RBF, BP, PSO, and RNN-CMAQ mentioned above. Representatively, a PM_2.5 prediction study using a multilayer perceptron artificial neural network predicted hourly PM_2.5 using data from an hour ago using six measurement stations in Poland [36]. PM_2.5 prediction studies using many ANNs, including the above studies, have focused only on hourly predictions, not daily predictions. Studies that predicted daily PM2.5 concentration by ANN are insufficient. In addition, when accurate weather forecasts are available, verification of performance changes of the forecasting model is not performed, so it is necessary to verify this.

Therefore, in this study, we developed a model that can predict each country nationwide and 16 administrative districts using ANN as a basic factor for air pollutant and meteorological data in Korea from 2015 to 2019. In addition, a one-day prediction model was developed, capable of next-day predictions of PM_2.5 concentration if the air pollution and weather information of the day is known. In addition, models that could predict PM_2.5 concentrations for NW and 16 administrative districts were developed using ANN.

2. Materials and Methods

2.1. Air Pollutants and Meteorological Data

In this study, as PM_2.5 observation in South Korea began in 2015, air pollutant data and meteorological data from 2015 to 2019 were used. Operational details of instruments and their locations are provided elsewhere [37]. Air pollutant data were collected from 487 sites in 16 regions of Korea from 1 January 2015, to 31 December 2019, provided by Air Korea (https://www.airkorea.or.kr/, accessed on 1 October 2022) (operated by Korea Environment Corporation, Incheon, South Korea) [38]. These comprise the daily averages and daily variance data estimated using hourly data. Air pollutant factors (PM₁₀, NO₂, SO₂, O₃, CO, and PM_2.5) were calculated with this data, which are daily averages and daily variances for nationwide (NW) and 16 administrative districts (AD; Seoul, Incheon, Gyunggi, Choongnam, Daejeon, Jeonbuk, GwangJu, Jeonnam, Gangwon, Choongbuk, Kyungbuk, Daegu, Ulsan, Kyungnam, Busam, and Jeju).

Meteorological data (temperature, humidity, wind speed, atmospheric pressure, precipitation, and snowfall) was provided by an automated synoptic observing system (ASOS) through Open Met Data Portal (https://data.kma.go.kr/, accessed on 1 October 2022) (operated by Korea Meteorological Administration, National Climate Data Center) [39]. The daily averages and variances were calculated for NW and AD based on 24 sites in the ASOS from 1 January 2015 to 31 December 2019. These daily average and variances were used as independent variables in the meteorological factors to predict next-day PM_2.5 concentration.

2.2. Artificial Neural Networks

In this study, models to predict the next-day PM_2.5 daily average for NW and AD were developed using an ANN. To develop prediction models using ANN, R version 4.1.0 was used with the “neuralnet” library. The variables in

Table 1. Variables for prediction model development.

Factors	Categories	Variables
Air Pollutant Factors (Daily Average)	PM10, NO2, SO2, O3, CO, PM2.5	x1, x2, x3, x4, x5, x6
Air Pollutant Factors (Daily Variance)	PM10, NO2, SO2, O3, CO, PM2.5	xv1, xv2, xv3, xv4, xv5, xv6
Meteorological Factors (Daily Average)	Temperature, Humidity, Wind Speed, Atmospheric Pressure, Precipitation, Snowfall	z1, z2, z3, z4, z5, z6
Meteorological Factors (Daily Variance)	Temperature, Humidity, Wind Speed, Atmospheric Pressure, Precipitation, Snowfall	zv1, zv2, zv3, zv4, zv5, zv6
Next-day PM2.5 (Daily Average)	PM2.5	y

were used to develop the models; y was used as a dependent variable, while the rest were used as independent variables.

PM_2.5 prediction model was developed separately for NW and AD. All independent variables are connected to the neurons in the hidden layer, which is composed of two columns, as shown in Figure 1. These neurons pass through the activation function and produce an output. In this study, a Logistic Function, Equation (1), was used as the activation function. Therefore, an optimal function is obtained when the neuron inputs are between 0 and 1, and the numerical independent variables of air pollutants and meteorological factors are converted into data between 0 and 1 through the min–max normalization of Equation (2) [40].

$$f\left(x\right)=\frac{1}{1+e^{-g\left(x\right)}}$$

(1)

$$Normalized data=\frac{Original data-X_{min} }{X_{max}-X_{min}}$$

(2)

The value that has passed through the neurons of the hidden layer is gathered in the output layer and calculated, and a response variable is subsequently derived. The error between the predicted and actual values is reduced, and the model is repeatedly learned. A model is learned to allow the partial derivative of the sum of squared error (SSE), which is the error function for the difference between the predicted and actual values derived from the model, to become smaller than the threshold [41]. This method is known as the “Rprop+” algorithm. Model learning is terminated when the absolute partial differential value of the SSE becomes smaller than the specified threshold or when the set number of training reaches 10⁶ [42].

ANN showed high prediction performance for time-series prediction in previous studies, but the ANN model could not entirely explain the relationship between the dependent and independent variables [43]. Therefore, the developed model should be verified using data not employed for model development. Two-thirds of the total data were used for model development (called “in-sample”) and the remaining data (called “out-of-sample”) were used for model validation. Two-thirds of each comprehensive air quality index category (good, normal, bad, and very bad) were randomly extracted and used as an in-sample (Tables S1 and S2). The decision to use a monthly factor to account for seasonal patterns affected the accuracy of the model. In addition, in Figure 1, the number of nodes and the number of hidden layers are shown, and this combination is called the hidden layer layout. The hidden layer layout should be optimized for best performance [44]. In addition, an appropriate threshold must be determined to prevent model overfitting.

Table 2. Levels of factorial design for artificial neural network model optimization.

Factor Name	Month	Hidden Layer Layout	Threshold
Factor Level	Included Not Included	6 × 6 12 × 12 24 × 24	0.01 0.05 0.1

shows the level of the factors used to determine the optimal ANN model. The presence or absence of the month factor, hidden layer layout, and threshold were tested and analyzed using a factorial design.

In the pre-experiment, at least three layers showed no significant performance improvement, and the use of one layer was not appropriate for the ANN [45]. Therefore, the number of layers was fixed at two (Table 2). The hidden layer layout is expressed as two, that is, n × n. The first n is the number of nodes in the first layer, and the second n is the number of nodes in the second layer. Generally, the number of nodes in each layer is the total number of independent variables or [log]₂ (the number of independent variables) [46,47]. Therefore, the factor level was set by reducing it by half from 24, which is the sum of 12 (total number of air pollutant factors) and 12 (total number of meteorological factors). The threshold value was found to overfit when the default value of R (0.01) was used. To prevent overfitting, the threshold values were tested with default values of 0.01, five times the default value of 0.05, and 10 times the default value of 0.1.

Eighteen (2×3×3) prediction models each for NW and AD were developed according to the level combination of the parameters in Table 2 using in-sample and verified by out-of-sample. Detailed model performance and verification results are presented in the next section.

2.3. Model Validation Metrics

To evaluate the performance of the prediction models, ‘R-squared’ and ‘absolute errors in n σ’ were used as model validation metrics. The absolute error in n σ’ is shown in Equation (3). First, the absolute errors between the actual measured value of PM_2.5, $y_i$, and the predicted value of PM_2.5, $\widehat{y_i}$ were calculated. Second, the percentage of absolute errors, $\left|\widehat{y_i}-y_i\right|$, that fell within n σ were calculated. The closer the absolute error of n σ’ is to 1, the more accurate the predictive model.

$$Absolute error in n \sigma =\frac{The number of data with absolute error<n \sigma }{Total number of data}$$

(3)

The standard of ‘Absolute Error in n σ’ is determined based on the standard deviation of PM_2.5. For a conservative judgment, 1 σ (standard deviation) was set to 12. As shown in

Table 3. Absolute error threshold for n σ.

	1 σ	0.5 σ	0.25 σ
Value	12	6	3

, the same threshold of ‘absolute error in n σ’ was set for both NW and AD.

3. Results and Discussion

3.1. Trend and Correlation Analysis for Input Parameter

Table 4. Statistical description of daily air pollutant factor, 2015–2019.

Factor	Average		Median		Min		Max		Standard Deviation
	NW	AD	NW	AD	NW	AD	NW	AD	NW	AD
PM10(μg/m3)	44.49	43.34	41.24	39.11	7.79	5.19	377.21	555.69	21.77	22.848
NO2 (ppm)	0.022	0.020	0.021	0.018	0.006	0.003	0.055	0.082	0.008	0.010
SO2 (ppm)	0.004	0.004	0.004	0.004	0.003	0.001	0.011	0.025	0.001	0.002
O3 (ppm)	0.028	0.029	0.027	0.028	0.006	0.001	0.074	0.092	0.011	0.012
CO (ppm)	0.490	0.477	0.457	0.446	0.277	0.113	1.058	1.485	0.129	0.151
PM2.5 (μg/m3)	24.634	24.633	22.573	21.917	3.393	1.045	106.897	140.793	12.243	13.898

displays the basic statistics of air pollutant factors for nationwide and administrative districts. Based on these, Table 4 and the South Korea comprehensive air quality index (Table S1), PM₁₀ and PM_2.5 have normal levels on an average, whereas NO₂, SO₂, O₃, and CO show good concentrations. However, the maximum values in Table 4 show harmfully high levels of PM₁₀ and PM_2.5, and bad levels of NO₂ and O₃ depending on the region. Table S2 provides in-depth details of the PM_2.5 factor, which is the response variable in this study. Over 80% of PM_2.5 daily averages were good or normal, whereas very bad concentrations were scarce.

Figure 2 shows the daily average of air pollutant data and the 30-day moving average of the daily average. Each air pollutant factor had a seasonal pattern; PM₁₀, NO₂, SO₂, and CO showed a decreasing trend every year, whereas O₃ showed an increasing trend. PM₁₀ was high in the winter and low in the summer. NO₂, SO₂, and CO also show patterns similar to those of PM₁₀. PM_2.5 also shows a similar pattern to PM₁₀, as shown in Figure 2. Conversely, O₃ was high in summer and low in winter.

Figure 3 shows the daily standard deviation of the air pollutant data and its 30-day moving average. A seasonal pattern in the standard deviation was also observed. As shown in Figure 3, the daily standard deviation of PM_2.5 varies seasonally, and the variance is large in winter and small in summer. As for NO₂, SO₂, and CO, the standard deviation in summer decreases each year. As shown in Figure 3 and, CO concentration and its standard deviation are high in winter, low in summer, and decreases every year. As shown in Figure 3, the standard deviation of O₃ was large in summer and small in winter. As shown in Figure 2 and Figure 3, PM₁₀, O₃, CO, and PM_2.5, all had large standard deviations when the daily average was high and small standard deviations when the daily average was low.

Table 5. Statistical description of daily meteorological factor, 2015–2019.

Factor	Mean		Median		Min		Max		Standard Deviation
	NW	AD	NW	AD	NW	AD	NW	AD	NW	AD
T (°C)	13.96	14.21	14.77	15.28	−10.47	−14.74	30.96	33.74	9.51	9.61
RH (%)	66.99	66.99	67.98	68.16	31.46	15.94	93.91	100.00	13.00	15.86
WS (m/s)	2.11	2.18	1.95	1.91	1.05	0.35	5.42	12.67	0.66	1.11
AP (hPa)	1009.63	1009.52	1009.87	1009.45	985.88	978.47	1029.04	1033.59	7.74	8.22
Precipitation (mm)	0.61	0.39	0.16	0.00	0.00	0.00	10.86	32.50	1.01	1.18
Snowfall (cm)	0.22	0.06	0.00	0.00	0.00	0.00	11.00	20.35	0.88	0.59

presents the basic statistics of the meteorological factors, where precipitation indicates the amount of rain per hour, and snowfall indicates the height of snow accumulation from the hourly indicator. Therefore, the daily average snowfall represents the average daily snow height from the ground. In the case of the daily average snowfall, there was a significant difference between administrative districts. Precipitation and snowfall were not observed meteorological phenomena due to the characteristics of the factor; therefore, the days when they do not occur have a value of 0, and the value of median is 0 or close to 0 because precipitation and snowfall are not observed for over half of the year.

Figure 4 shows the daily average and 30-day moving average of the meteorological data. Each meteorological factor exhibited a seasonal pattern. Temperature, humidity, and precipitation were high in summer and low in winter, and from the wind speed and atmospheric pressure are high in winter and low in summer. Snowfall is observed in winter due to its seasonal characteristics.

Figure 5 shows the daily standard deviation of the meteorological data and 30-day moving average. In the standard deviation, seasonal patterns similar to the daily average patterns were observed. As shown in Figure 5, the standard deviations of temperature, humidity, wind speed, and atmospheric pressure are small in summer and large in winter, and the standard deviation in precipitation is large in summer and small in winter. Snowfall is observed exclusively in winters, the standard deviation appears only during winter.

Because the air pollutant factor is known to affect the occurrence of PM_2.5 and meteorological factors reflect seasonal changes, they are appropriate as independent variables in the prediction of PM_2.5. To examine their relationship in greater depth, the correlation between the air pollutants and meteorological factors and the next-day PM_2.5 concentration was analyzed. Independent and dependent variables used to develop the prediction model are summarized in Table 1. Air pollutant and meteorological factors were independent variables, and next-day PM_2.5 concentration was the dependent variable to be predicted. As correlations using NW data and AD data are very similar, only the correlation with NW data is presented.

Results of correlation analysis for next-day PM_2.5 and air pollutant factors are summarized in

Table 6. Correlations among next-day PM_2.5 and air pollutants (nationwide daily average and variance).

	x1	x2	x3	x4	x5	x6	xv1	xv2	xv3	xv4	xv5	xv6	y
x1	1.00	0.56	0.56	0.09	0.61	0.81	0.55	0.53	0.19	0.25	0.44	0.64	0.57
x2		1.00	0.68	−0.38	0.85	0.69	0.07	0.90	0.16	0.10	0.75	0.45	0.62
x3			1.00	0.03	0.58	0.61	0.08	0.69	0.55	0.33	0.58	0.35	0.52
x4				1.00	−0.41	0.02	0.00	−0.13	0.31	0.66	−0.49	−0.03	−0.02
x5					1.00	0.79	0.12	0.69	0.01	−0.04	0.87	0.60	0.63
x6						1.00	0.20	0.63	0.20	0.31	0.58	0.78	0.71
xv1							1.00	0.06	0.01	−0.01	0.10	0.27	0.14
xv2								1.00	0.28	0.32	0.62	0.42	0.58
xv3									1.00	0.47	0.03	0.07	0.15
xv4										1.00	−0.15	0.13	0.23
xv5											1.00	0.50	0.46
xv6												1.00	0.49

Bold character represents significant correlation with significant level 0.05.

. The daily average concentrations of PM10 (0.57), NO₂ (0.62), SO₂ (0.52), CO (0.63), and PM_2.5 (0.71), which are air pollutants excluding O₃ (−0.02), showed a high positive correlation with next-day PM_2.5. In addition, next-day PM_2.5 had a positive correlation with the variances of the air pollutants, and had a positive correlation with NO₂ (0.58), CO (0.46), and PM_2.5 (0.49). Based on the correlation analysis results, using daily variances of air pollutants as independent variables is, thereby, reasonable.

Table 7. Correlations among next-day PM_2.5 levels and meteorological factors (nationwide daily average and variance).

	z1	z2	z3	z4	z5	z6	zv1	zv2	zv3	zv4	zv5	zv6	y
z1	1.00	0.56	−0.22	−0.80	0.24	−0.39	−0.31	−0.30	−0.32	−0.25	0.22	−0.24	−0.31
z2		1.00	−0.25	−0.51	0.48	−0.14	−0.60	−0.60	−0.16	−0.03	0.24	−0.09	−0.21
z3			1.00	−0.08	0.11	0.19	−0.18	0.07	0.87	0.53	0.00	0.14	−0.32
z4				1.00	−0.30	0.25	0.39	0.24	0.03	−0.03	−0.19	0.13	0.29
z5					1.00	−0.03	−0.36	−0.34	0.21	0.29	0.70	−0.01	−0.26
z6						1.00	0.02	0.08	0.23	0.07	−0.04	0.84	0.05
zv1							1.00	0.63	−0.14	−0.02	−0.17	0.01	0.40
zv2								1.00	0.03	0.06	−0.20	0.05	0.30
zv3									1.00	0.60	0.03	0.16	−0.27
zv4										1.00	0.04	0.03	−0.07
zv5											1.00	−0.02	−0.13
zv6												1.00	0.02

Bold character represents significant correlation with significant level 0.05.

shows the correlation between next-day PM_2.5 and meteorological factors. In terms of the daily average, next-day PM_2.5 was positively correlated with atmospheric pressure (0.29) and snowfall (0.05). Temperature (−0.31), humidity (−0.21), wind speed (−0.32), and precipitation (−0.26) were negatively correlated with next-day PM_2.5. In terms of daily variance, next-day PM_2.5 was positively correlated with temperature (0.40), humidity (0.30), and snowfall (0.02), and negatively correlated with the rest of the factors. In general, meteorological factors had lower correlations than air pollutant factors but were used for prediction model development as important independent variables showing seasonal changes.

3.2. PM_2.5 Prediction Model for Nationwide

According to the factor levels in Table 2, 18 prediction models were developed NW.

Table 8. ANOVA table of nationwide PM_2.5 prediction model.

Factor	Degree of Freedom	Sum of Squares	Mean Squares	F Value	Pr(>F)
Month	1	0.011243	0.011243	17.37643	0.014048
Hidden Layer Layout	2	0.05415	0.027075	41.84383	0.002081
Threshold	2	0.224784	0.112392	173.6985	0.00013
Month Factor: Hidden Layer Layout	2	0.001712	0.000856	1.322687	0.362311
Month Factor: Threshold	2	0.029913	0.014957	23.11483	0.006342
Hidden Layer Layout: Threshold	4	0.148298	0.037075	57.29761	0.000873
Residuals	4	0.002588	0.000647	-	-

shows the analysis of variance (ANOVA) table that statistically explains the factorial design experiment results. The response variable in this table is the R-squared of the out-of-sample. Based on a significance level of 0.05, all main effects (hidden layer layout, month, and threshold) affected R-squared. Two interaction effects (month factor and hidden layer layout, and hidden layer layout and threshold) also affected R-squared. Therefore, three factors affected the predictive model. This shows that it is appropriate to find the optimal model according to level change.

Figure 6a,b show in-sample/out-of-sample R-squared of the 18 prediction models developed according to factorial design, respectively. The higher the R-squared value was, the better the predictive ability of the model was. However, to avoid overfitting, the difference in R-squared between in-sample and out-of-sample should be minimal. Thus, to prevent overfitting, the model with a high average R-squared (average R-squared for in-sample and out-of-sample) was selected as the optimal model among the models in which the in-sample and out-of-sample R-squared differed within 10%. Using the month factor showed higher R-squared, and in-sample R-squared decreased as the threshold increased. However, if the threshold increased from 0.01 to 0.05 or 0.1, the deviation of R-squared between in-sample and out-of-sample decreased, thereby reducing the overfitting problem. Therefore, with the overfitting problem reduced, the model with the highest average R-squared (month factor: included, hidden layer layout: 24 × 24, threshold: 0.05) was determined as the optimal model. Assuming that the weather prediction is accurate, if the meteorological factor on the forecasting day is used instead of data from the previous day, the R-squared increased from 0.65 to 0.81 for in-sample and from 0.64 to 0.73 for out-of-sample as shown in

Table 9. R-squared and absolute errors in n σ of nationwide model with/without accurate weather forecasting (Month factor: included, hidden layer layout: 24 × 24, threshold: 0.05).

	Without Accurate Weather Forecasting		With Accurate Weather Forecasting
	In-Sample	Out-of-Sample	In-Sample	Out-of-Sample
R-squared	0.65	0.64	0.81	0.73
Absolute Error in 1 σ	0.91	0.91	0.96	0.92
Absolute Error in 0.5 σ	0.66	0.64	0.81	0.75
Absolute Error in 0.25 σ	0.40	0.37	0.50	0.46

. The absolute error n σ also increased, indicating that the accuracy of the model could be further improved if accurate weather predictions were used.

The predicted and actual values of the optimal prediction model are presented in Figure 7. The distribution of most of the results proximate to the centerline indicates that the model adequately predicted PM_2.5. Figure 7b has a slightly smaller difference between the predicted and the measured values than Figure 7a.

3.3. PM_2.5 Prediction Model for Administrative Districts

The PM_2.5 prediction model for AD, was developed in the same way as the NW PM_2.5 prediction model. As shown in

Table 10. ANOVA table of PM_2.5 prediction model for administrative districts.

Factor	Degree of Freedom	Sum of Squares	Mean Squares	F Value	Pr (>F)
Month Factor	1	3.56 × 10−5	3.56 × 10−5	0.2.50 × 10−1	6.27 × 10−1
Hidden Layer Layout	1	6.55 × 10−3	6.55 × 10−3	46.11	2.99 × 10−5
Threshold	1	2.88 × 10−3	2.88 × 10−3	20.30	8.94 × 10−4
Month Factor:Hidden Layer Layout	1	2.09 × 10−4	2.09 × 10−3	1.47	2.51 × 10−1
Month Factor:Threshold	1	7.40 × 10−6	7.40 × 10−6	5.21 × 10−2	8.24 × 10−1
Hidden Layer Layout:Threshold	1	3.79 × 10−3	3.79 × 10−3	26.70	3.10 × 10−4
Residuals	11	1.56 × 10−3	1.42 × 10−4	-	-

, based on a significance level of 0.05, the two main effects of the hidden layer layout and the threshold were significant, and they were also the most significant among all the interaction effects. Unlike the NW analysis, the month factor was not clearly significant in the ANOVA.

As with the NW prediction model, the model with the month factor had higher overall R-squared than the model without the month factor (Figure 8). Although it is not as sharp as the NW model in Figure 6, the in-sample R-squared value decreased as the threshold increased. As the number of nodes in the hidden layer layout decreased and the threshold increased, Figure 8 describes that the deviation between the in-sample and out-of-sample R-squared values decreased, and the overfitting problem also reduced. Therefore, the model with the highest average R-squared value and a less than 10% difference between in-sample and out-of-sample R-squared values was selected as the optimal PM_2.5 prediction model. Thus, when the month factor was included, the number of nodes in the hidden layer layout was 12, and the threshold was 0.05.

Table 11. R-squared and absolute errors in n σ of administrative district model with/without accurate weather forecasting (month: included, hidden layer layout: 12 × 12, threshold: 0.05).

	Without Accurate Weather Forecasting		With Accurate Weather Forecasting
	In-Sample	Out-of-Sample	In-Sample	Out-of-Sample
R-squared	0.65	0.55	0.73	0.65
Absolute Error in 1 σ	0.88	0.84	0.91	0.89
Absolute Error in 0.5 σ	0.62	0.58	0.68	0.65
Absolute Error in 0.25 σ	0.34	0.33	0.39	0.38

shows the R-squared and absolute errors in n σ of the optimal PM_2.5 prediction model for AD (month factor: included, hidden layer layout: 6 × 6, threshold: 0.05). As shown in Figure 8 and Table 5, the accuracy of the PM_2.5 prediction model for AD is slightly lower than that of the PM_2.5 NW prediction model. R-squared of PM_2.5 prediction model without weather forecasting for AD are 0.65 (in-sample) and 0.55 (out-of-sample), and the absolute error in 1 σ is 88% and 84%, respectively. Assuming that the weather prediction is accurate, if the meteorological factor on the forecasting day is used instead of data from the previous day, The R squared increased from 0.65 to 0.73 for in-sample and from 0.55 to 0.65 for out-of-sample. The accuracy of the NW PM_2.5 prediction model can be improved with high accuracy weather forecasting.

Figure 9 presents the predicted and measured values of the optimal PM_2.5 prediction model for the AD. PM_2.5 in each region is accurately predicted without considering regional variables. Figure 9b has a slightly smaller difference between the predicted and measured values than Figure 9a. In future studies, a regional variable should be considered or a regional model should be developed separately to further improve the predictive power of the model.

Next-day PM_2.5 prediction models are compared in

Table 12. Next-day PM2.5 prediction model performance comparison.

	Data	Methodology	R-Squared	MAE
This study	Precipitation, Humidity, Wind speed, Atmospheric Pressure, Precipitation, Snow fall, PM10, NO2, SO2, O3, CO, PM2.5	Multi-layer Perceptron(ANN)	0.73	4.59
McKendry, 2002 [34]	Temperature, Precipitation, PM10, NO, NO2, O3, PM2.5	Multi-layer Perceptron(ANN)	0.56	-
Sun and Sun, 2017 [35]	Temperature, PM10, NO2, SO2, O3, CO, PM2.5	LSSVM(Least square support vector machine), Cuckoo search, GRNN	-	18.84

. The PM_2.5 prediction model developed in this study is superior to the two preceding studies in terms of R-squared and mean absolute error (MAE). However, since the data used in each study is different, it may be inappropriate to compare only R-squared and MAE.

4. Conclusions

In this study, the correlation between the daily averages and daily variances of air pollutants and meteorological factors was analyzed with next-day PM_2.5 concentrations. Through this, it was confirmed that next-day PM_2.5 concentration was not only influenced by the daily average of air pollutant data and meteorological data but also by the daily variances.

The data were divided into two types: NW data and administrative district data (16 regions). Subsequently, daily averages and variances of air pollutant data (PM₁₀, NO₂, SO₂, O₃, CO, and PM_2.5) and meteorological data (temperature, humidity, wind speed, atmospheric pressure, precipitation, and snowfall) were calculated. A prediction model that determined next-day PM_2.5 was developed using an ANN. Factorial design was used to find the best factor level (month, hidden layer layout, and threshold) for the ANN, and the optimal model was selected based on ANOVA. The absolute error in 1 σ of the PM_2.5 NW prediction model is 91% (in-sample 91%, out-of-sample 91%), and that for AD is 86% (in-sample 88%, out-of-sample 84%). Assuming that the weather forecast was accurate, the accuracy of these prediction models (absolute error in 1 σ) increased up to 96% (in-sample) and 92% (out-of-sample) for NW and 91% (in-sample) and 89% (out-of-sample) for the AD.

Our developed model has a significant advantage over traditional predictive models in that it uses the air pollutions and meteorological data of the current day to forecast the PM_2.5 for the next day. This is more convenient than conventional models that rely on statistical analysis or air pollution modeling, such as CMAQ. Regions such as South Korea, where haze events are common, experience daily PM_2.5 concentration fluctuations of more than three times during the event [19]. As a result, it is crucial to have a model that can provide people with an action plan to prepare for these daily changes. Our study confirmed the accuracy of the NW model, and we plan to conduct an optimization study of the AD model, which is relatively inaccurate, in future research.