Development of Air Pollution Forecasting Models Applying Artificial Neural Networks in the Greater Area of Beijing City, China

1. Introduction

Today's way of life, as it has been shaped by the existing social and economic conditions, requires the continuous exposure of man to an atmosphere with adverse effects on his health. Research findings from all over the world converge in terms of the destructive consequences, that the burdened atmospheric air has on humans, agriculture and infra-structure. The continuous degradation of the climate makes the need of finding a means of predicting the quality of the atmosphere, as well as dealing with the production of atmospheric pollutants, imperative.

Air pollution is defined as the "contamination of the indoor or outdoor environment by any chemical, physical or biological agent that modifies the natural characteristics of the atmosphere."[1]. The effects of air pollution have been studied in many countries, both within and out-side the EU, with each research confirming its catalytic role in the degradation of the quality of life. Exposure to PM₁₀ was found to increase the likelihood of hospitalization for bronchitis symptoms, both for adults and children [2], while exposure to excess concentrations of PM_2.5 was found to be a cause of hospitalization for cardiovascular and respiratory causes, as well as cause of death [3,4]. Also, exposure to this type of particles can negatively affect infants, even in the prenatal stage, increase the probability of birth defects, obesity, type I diabetes, neurological and behavioral dysfunctions, premature birth and even neonatal death [5,6,7,8]. Equally important are the excessive concentrations of sulfur dioxide (SO₂), as an excess of 10 ppb can increase the number of hospitalizations by 1.7% [8]. Prenatal and postnatal exposure to nitrogen dioxide (NO₂) leads to increased chances of bronchopulmonary infections, pneumonia as well as obesity [6,9]. Research that was done in areas of Athens (Thrakomakedones and Athens center) for the period 2001-2018, showed that 6% and 7.5% of deaths in these areas respectively, are due to increased concentrations of ozone (O₃) [10].

However, the effects of air pollution are not limited to human health. Extensive research carried in the city of Beijing, China showed a direct correlation between the concentration of ozone (O₃) as well as nitrogen oxides (NOx) and the reduction of the amount of grain yielded. The percentages reach up to 15%, while it is predicted that they will reach the height of 23% in the coming years [11]. Correspondingly harmful are the effects on infrastructure due to acid rain as well as the transportation sector. In particular, after research carried out by Hernández et al [12] regarding the effect of this on car paint, it was found that between the two aging methods, Xenon and a mixture of acid rain, the latter had the most destructive consequences. Finally, Ibrahim et al. [13] in their research on the surface treatment of concrete, after exposure to an acidic environment, report the phenomenon of gypsum formation and its destructive properties on building materials, gradually weakening the ability of cement to withstand compression.

The need to design a means of forecasting pollutant concentrations is imperative. Over time, many researchers have tried to design such predictive models. In 2015 Xiao Feng et al. [14] created a model that combined an MLP neural network with a geographical model based on the air trajectory and the use of the wavelet transformation method to forecast the average daily PM_2.5 concentration for the next two days in Beijing, China. Similar efforts were made by Madhavi Anushka Elangasinghe et al. [15], in 2014, to forecast the hourly concentration of nitrogen dioxide (NO₂), using an MLP neural network with one hidden layer, trained with the Levenburg Marquardt algorithm, for the Auckland, New Zealand region. In 2016 Yun Bai et al.[16] using the static wavelet transform method and the training of an ANN with a back-propagation algorithm, tried to predict the daily concentrations of PM₁₀ particles and the concentrations of sulfur dioxide (SO₂) and nitrogen dioxide (NO₂). In 2017 Fabio Biancofiore et al. [17] also tried to predict the average daily concentrations of PM_2.5 and PM₁₀ particles for the next one to three days, while in 2018 Fabiana Franceschi et al. [18] tried through a statistical study and AΝΝ integration to predict the concentrations of PM_2.5 and PM₁₀ particles in Bogotá, Colombia. According to further research published in 2024, Quanchao Chen et al. [19] designed an innovative model for the prediction of hourly concentrations for PM_2.5 and PM₁₀ as well as ozone (O₃), in the city of Beijing, by creating an AAMGCRN (Adaptive Adjacency Matrix Graph Convolutional Recurrent Network). Accordingly, Sarmad Dashti Latif et al. [20] applied multiple machine learning methods to predict the ozone (O₃) concentration for the next 1, 3, 5 and 7 hours in the Klang Valley, Malaysia.

This research was conducted in an attempt to design a universal air pollution forecasting model. It is also mentioned that over the course of a decade, no corresponding studies have been found which use strictly meteorological variables and no other pollutants as training data. The latest reference is in 2014, in the forecasting model created by Madhavi Anushka Elangasinghe et al. [15], who argued that models in which the inputs consist, among other things, of pollutant concentrations, have limited practical use.

2. Materials and Methods

The present study addresses a wide range of atmospheric pollutants, specifically the concentrations of suspended particulate matter with an aerodynamic diameter of 2.5μm (PM_2.5) and 10μm (PM₁₀), as well as the concentration of sulfur dioxide (SO₂), nitrogen dioxide (NO₂), carbon monoxide (CO) and ozone (O₃).

The area of interest is the city of Beijing, China and specifically 12 sub-districts within it. ANNs were developed and used to achieve the requested results. ANNs are a sub-field of Machine Learning (ML) and what sets them apart from other ML techniques is the special way in which they create their systems. ANNs, as their name suggests, try to imitate both the structure and the way of operation of the human brain [21]. Specifically, they consist of artificial neurons, with “nerves” providing them with the required information (input data). The inputs when entering the neuron are multiplied by some "weights" (factors that reduce or enhance the effect that each input has on the final outcome) and after passing through a transfer function, they exit from it (output data) [22]. The schematic representation of the above process is presented in Figure 1.

The ANNs that were developed in this work are Multi-Layer Perceptron (MLP) and they stand out for the existence of hidden layers (Figure 2). Simple “perceptrons” use no hidden layers making their use limited due to a lack of credibility. MLP however by using multiple hidden layers can process data much faster and efficient than their predecessors. Their topology and training parameters play a vital role, where if they are not adjusted properly, they can make the training process unsuccessful. If the number of hidden layers is lacking then the training process will be incomplete and the credibility of the final ANN low. However, if the number of hidden layers exceeds the required amount, then the ANN may produce results of high credibility for the current dataset, but will not work properly on different datasets. That’s because of a phenomenon called overfitting or overtraining, where the ANN training process failed making the ANN to replicate, not predict, the exact values of the testing and validation dataset [21].

The way in which the processing of the input data is carried out and their correlation with the output data, make this particular processing method ideal for cases of creating forecasting models. In particular, the present work is called upon to create and evaluate a sufficient number of forecasting ANNs models, in order to select those that present the best predictive ability.

2.1. Study Area and Data Availability

The study area is the city of Beijing, China (39° 54′ 13″ N, 116° 23′ 17″ E) for which hourly measurements of the concentrations of the pollutants of interest as well as meteorological conditions were collected for the time period 1/3/2013 to 28/2/2017. The corresponding values were obtained from a free dataset by Chen Song [24] and were obtained through the link below “https://archive.ics.uci.edu/dataset/501/beijing+multi+site+air+ quality+data”. The following data were given:

• Concentration of particulate matter with an aerodynamic diameter of up to 2.5 micrometers, PM_2.5.
• Concentration of particulate matter with an aerodynamic diameter of up to 10 micrometers, PM₁₀.
  • Concentration of sulfur dioxide, SO₂.
  • Concentration of nitrogen dioxide, NO₂.
  • Concentration of carbon monoxide, CO.
  • Ozone concentration, O₃.
  • Ambient air temperature, TEMP.
  • Dew temperature, DEWP.
  • Atmospheric pressure, PRES.
  • Height of rain, RAIN.
  • Wind speed, WSPM.
  • Wind Direction, Wd.

The above values were available for nine (9) total locations of Beijing, namely:

• Location 1 : Aotizhongxin
• Location 2 : Changping
• Location 3 : Dongsi
• Location 4 : Guanyuan
• Location 5 : Gucheng
• Location 6 : Nongzhanguan
• Location 7 : Tiantan
• Location 8 : Wanliu
• Location 9 : Wanshouxigong

The above locations are also shown in Figure 3 (locations with an asterisk). Then, it was decided to be chosen the distance between the examined locations to be no more than 20 kilometers (km). This decision was based on the assumption that within the distance of 20km the influence of the examined locations to each other will be significant as well as the selected locations to be closer to the city’s center. Before any data processing it was necessary to be checked the available data sets for non-available/missing values.

All preliminary screening was done using Microsoft Excel 2021. For example, in Table 1 the data completeness for location 3 is presented. In total, in all nine (9) areas, more than 7000 missing values were found out of a total of 420780 items in each area. Standard methodology dictates that when checking the data for missing values, the researcher is advised to delete the entire row in which they were located. However, such a treatment is possible when there is a large number of available data and/or a small number of missing values. In cases such as in the specific data set, which is not of sufficient size, if the specific methodology was applied, it would lead to a data reduction of 20%. Therefore, it was decided not to follow the specific directive and to make an attempt to cover the missing data through a combination of various methods which are analyzed below.

2.1.1. Method 1: Using Existing Values & Microsoft Excel Commands

In order to apply this method, a basic assumption is made, that the consecutive values within 5 hours do not differ greatly from each other. Having made this assumption renders what must be done quite simple. Initially a check is made for the existence of values within the previous 5 hours and within the next 4 hours. From this check, four (4) individual scenarios emerge as follows:

1. Existence of both values, within the given time limits. In this case the missing value is the average of the two existing values.

2. Existence of only the previous value, within the time limits. In this case the missing value is equal to the previous value plus/minus a certain number, which is listed in Table 2 below.

3. Existence of only the next value, within the time limits. In this case the missing value is equal to the next value plus/minus a specific number, which is listed in Table 2 below.

4. Simultaneous absence of the two values, within the time limits. In this case the element receives the value "NA", so that it can be processed later.

Although the above method is quite effective, it is not able to cover 100% of the missing values, however, it presents an average efficiency of more than 60%. The number of missing values covered are presented in detail in Table 3.

2.1.2. Method 2: Development of a Code within the MATLAB Programming Environment

This method also requires an assumption that the concentrations of pollutants and the values of meteorological factors do not change significantly in an area of about ten (10) kilometers, or less. Initially, the distance between the nine (9) study areas is calculated and for each one the closest areas are selected. Let's take location 3 (Dongsi) as an example. If the distances of the other locations are calculated in relation to location 3, it is found that locations 6,4,8 and 1 (in order of proximity) are within a range of 10 km or less. It is logical that the values of the areas closest to location 3, have a greater influence on the values of interest. In the next step, the relative position of locations 1,4,6 and 8 with respect to location 3 (North, East, North-East, etc.) needs to be determined. Finally, the appropriate code was written within the MATLAB environment, version R2022a, based on which the wind direction is taken into account and the appropriate location is selected based on this. In each case, the missing value in location 3 gets exactly the same value as the corresponding value of the selected area. This method, though much more complicated and detailed than the first one, does not cover a large number of missing values, with a success rate of less than 20%. The remaining values are once again set to “NA” so as to be processed at a later time.

Table 2. Addition and subtraction numbers for each pollutant and meteorological factor.

Variable	Additions/Subtractions Number
PM2.5	1
PM10	1
SO2	0.5
NO2	0.5
CO	50
O3	0.5
TEMP	No additions or subtractions were needed.
PRES	No additions or subtractions were needed.
DEWP	No additions or subtractions were needed.
RAIN	No additions or subtractions were needed.
wd	No additions or subtractions were needed.
WSPM	No additions or subtractions were needed.

Table 2. Addition and subtraction numbers for each pollutant and meteorological factor.

Variable	Additions/Subtractions Number
PM2.5	1
PM10	1
SO2	0.5
NO2	0.5
CO	50
O3	0.5
TEMP	No additions or subtractions were needed.
PRES	No additions or subtractions were needed.
DEWP	No additions or subtractions were needed.
RAIN	No additions or subtractions were needed.
wd	No additions or subtractions were needed.
WSPM	No additions or subtractions were needed.

2.1.3. Method 3: Applying the Linear Regression Methodology

The ideology of this method is directly related to the basic idea behind Method 2. Same as before, the basic assumption here is that the meteorological and atmospheric conditions prevailing in nearby areas, describe with relative accuracy the conditions in the study area. First, the areas are categorized in order of proximity. Then their graphical representation is carried and is followed by the extraction of graphs, structured so that the linear correlation between the values is evident. Finally, these linear equations are extracted and used in order of proximity in the missing values of each region. This method offers 100% coverage of the remaining “NAs”. Figure 4 shows indicatively the graphs concerning the linear correlation between PM_2.5 concentrations for location 3 in relation to locations 1,4,6, and 8 respectively.

2.2. Data Preparation

Before the training process of the ANNs can begin, the appropriate processing of the input data was necessary. Initially, it was necessary to be checked the correlation of the variables-data, in order to reveal any existing relationships amongst them. Therefore, the correlation coefficient between the variables was calculated, for each region and in the end the average of them is taken into account as presented in Table 3. However, despite the attempt to extract these "hidden" relationships through the correlation coefficient, Table 3 does not offer much insight. As an alternative method for determining optimal combinations, the Principal Components Analysis (PCA) technique was used, in combination with the k-means clustering method, which showed that 40% of the information can be described solely with the set of temperatures. In practice, however, such a thing is not valid. Although based on methodology we should be satisfied only with the results of the PCA analysis, in the present paper further scenarios are analyzed, which proved to be better than the proposed one. After all, Fabiana Franceschi et al. [18] found a positive correlation between PM₁₀ concentration and wind direction, while a negative correlation was observed between the concentration of the same pollutant in terms of temperature and wind speed. These findings are further reinforced by Zhang et al. [25] in earlier research, in Beijing city, China. Accordingly, for PM_2.5, a positive correlation was observed between them and relative humidity [18], which is also verified by this specific research work.

Table 3. Table of mean correlation coefficients.

	PM2.5	PM10	SO2	NO2	CO	O3	TEMP	PRES	DEWP	RAIN	wd	WSPM	RH
PM2.5	1.00	0.88	0.48	0.68	0.79	-0.16	-0.14	0.01	0.11	-0.01	-0.12	-0.27	0.39
PM10		1.00	0.46	0.66	0.70	-0.13	-0.11	-0.02	0.06	-0.02	-0.07	-0.18	0.26
SO2			1.00	0.49	0.54	-0.17	-0.34	0.22	-0.28	-0.03	-0.05	-0.10	-0.08
NO2				1.00	0.71	-0.50	-0.29	0.14	-0.03	-0.03	-0.15	-0.42	0.33
CO					1.00	-0.32	-0.34	0.18	-0.07	-0.01	-0.14	-0.29	0.34
O3						1.00	0.60	-0.45	0.32	0.02	0.14	0.29	-0.27
TEMP							1.00	-0.83	0.82	0.06	0.02	0.03	0.10
PRES								1.00	-0.77	-0.01	0.00	0.08	-0.24
DEWP									1.00	0.10	-0.11	-0.28	0.63
RAIN										1.00	-0.01	0.12	0.10
Wd											1.00	0.24	-0.22
WSPM												1.00	-0.52
RH													1.00

Table 3. Table of mean correlation coefficients.

	PM2.5	PM10	SO2	NO2	CO	O3	TEMP	PRES	DEWP	RAIN	wd	WSPM	RH
PM2.5	1.00	0.88	0.48	0.68	0.79	-0.16	-0.14	0.01	0.11	-0.01	-0.12	-0.27	0.39
PM10		1.00	0.46	0.66	0.70	-0.13	-0.11	-0.02	0.06	-0.02	-0.07	-0.18	0.26
SO2			1.00	0.49	0.54	-0.17	-0.34	0.22	-0.28	-0.03	-0.05	-0.10	-0.08
NO2				1.00	0.71	-0.50	-0.29	0.14	-0.03	-0.03	-0.15	-0.42	0.33
CO					1.00	-0.32	-0.34	0.18	-0.07	-0.01	-0.14	-0.29	0.34
O3						1.00	0.60	-0.45	0.32	0.02	0.14	0.29	-0.27
TEMP							1.00	-0.83	0.82	0.06	0.02	0.03	0.10
PRES								1.00	-0.77	-0.01	0.00	0.08	-0.24
DEWP									1.00	0.10	-0.11	-0.28	0.63
RAIN										1.00	-0.01	0.12	0.10
Wd											1.00	0.24	-0.22
WSPM												1.00	-0.52
RH													1.00

2.3. Scenarios Creation

The scenarios that were created were the same for each location, however each of them was studied separately. The goal was to train ANNs forecasting models, for each location and merge them into a universal algorithm. Each location “includes” six (6) pollutants (PM_2.5, PM₁₀, SO₂, NO₂, CO and O₃), each pollutant consists of eight (8) scenarios, and each scenario includes ten (10) different ANNs models. The total amount of the developed ANNs was 4320 forecasting models. The training data includes a scenario-different combination of meteorological variables of the hourly values, during the three previous days and predicts the next 24-hourly concentrations. More specifically, in this work the developed ANNs models are able to forecast the hourly air pollutant concentration for the next 24-hours, based on the hourly values from the previous three (3) days. To make it more understandable, let's assume that today is Sunday. At any hour on Sunday, the developed ANNs models are able to give the concentration ​​of each pollutant for the next 24-hours (hourly forecasting step) of Monday (next day forecasting horizon). In any case, the hourly values ​​of the necessary parameters (see scenarios- Table 4) of the three previous days, that is Thursday, Friday and Saturday, are taken into account. The specific structure gives to the developed ANNs forecasting models an operational interest since the forecast can be made at any time during the day, for the next day, giving an advantage in making correct, valid and timely decisions by the competent agencies.

For a better study and analysis of the data, it was considered appropriate to add one more variable, relative humidity (RH), as it combines the dew point temperature (DEWP) and dry bulb temperature (TEMP) data. The developed scenarios are described in Table 4. RH was calculated using the Equation (1) [26]:

$$\mathrm{RH}={\displaystyle \frac{{\mathrm{e}}^{(17.625\text{-}\mathrm{DEWP}/243.04+\mathrm{DEWP})}}{{\mathrm{e}}^{(17.625\text{-}\mathrm{TEMP}/243.04+\mathrm{TEMP})}}}$$

(1)

As mentioned, for each scenario, 10 different ANNs were trained, which were then evaluated and the best one was selected. For reasons of repeatability of the experiment, the architecture of the developed ANNs is listed in Table 5. The training functions were chosen so that a secondary evaluation, of the way in which the training process can be optimized, can be executed. Specifically, the software’s default training function (Levenburg Marquardt) was chosen as the function to create the first ANN, while its individual parameters were adjusted to require "medium" computational power. For the next four (4) ANNs, they were chosen to be trained with the Bayesian Regularization training algorithm, as it is suitable to train ANNs with the aim of pattern recognition. ANNs number 6 to 10 are examples of other train functions, which were chosen in an effort to find possible functions with better performance. Among the ten (10) developed ANNs models, the first 5 proved to be the most "demanding", as they need a lot of computational power. However, as will be presented in the next section, they consistently offered the most valid results. On the contrary, the second half of Table 5, although it was less "demanding", provided very unstable results, with close to zero utilization capability. However, it is worth mentioning that none of the last five (5) training functions are suitable for training ANNs models of this kind. The topologies/architectures of the developed ANNs models were created in such a way that they could be evaluated by the same standards, while allowing the training process to be commenced by a conventional desktop computer.

Furthermore, the initial dataset was split (randomly) in 3 subsets. The first was the training subset containing 70% of the total data volume, the second was the cross-validation subset and the third was the testing subset containing 15% of the total data volume each one, respectively. Finally, for all of the ten developed ANNs of Table 5, the number of training epochs was equal to 200.

2.4. Software and Infrastructure

The following software were used for the preparation of this work:

• MATLAB R2022a
• Microsoft Excel 2021

The ANNs training was carried out on a home desktop computer with the following specifications:

• CPU: AMD Ryzen 7 5700G
• RAM: G.Skill Ripjaws V 16GB DDR4-3200MHz
• GPU: N/A
• SSD Kingston NV1 500GB M.2 NVMe (SNVS/500G).

In order to be able to evaluate the above neural networks, it was deemed necessary to calculate eight (8) statistical indices [27]. These indices and their equations are listed below: The Equations (2) through (5) describe the statistical evaluation indices for the performance of the models in order to predict the next 24-hourly concentrations, whereas Equations (6) through (9) represent the evaluation indices, that determine the predictive ability of each developed ANN model regarding a certain threshold. More specifically, if the developed model is able to predict the exceedances, in other words the cases where the pollutant concentration was over a specific threshold value or not. These threshold concentrations were determined by the reference values for each pollutant according to WHO. [28]

Mean Absolute Error (MAE)	$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{\mathrm{n}}}·{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}}\left|\left({\mathrm{P}}_{\mathrm{i}}\text{-}{\mathrm{O}}_{\mathrm{i}}\right)\right|$	(2)
Root Mean Square Error (RMSE)	$\mathrm{RMSE}=\sqrt[2]{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}}{\displaystyle \frac{{\left({\mathrm{P}}_{\mathrm{i}}\text{-}{\mathrm{O}}_{\mathrm{i}}\right)}^2}{\mathrm{n}}}}$	(3)
Pearson’s Correlation Coefficient (R)	$\mathrm{R}={\displaystyle \frac{1}{\mathrm{n}}}·{\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}\left[\left({\mathrm{P}}_{\mathrm{i}}\text{-}{\mathrm{P}}_{\mathrm{mean}})·({\mathrm{O}}_{\mathrm{i}}\text{-}{\mathrm{O}}_{\mathrm{mean}}\right)\right]}{\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left[{\left({\mathrm{O}}_{\mathrm{i}}\text{-}{\mathrm{O}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}\right)}^2\right]}·\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left[{\left({\mathrm{P}}_{\mathrm{i}}\text{-}{\mathrm{P}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}\right)}^2\right]}}}$	(4)
Index of Agreement (IA)	$\mathrm{IA}={\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}\left[{\left({\mathrm{P}}_{\mathrm{i}}\text{-}{\mathrm{O}}_{\mathrm{i}}\right)}^2\right]}{\sum _{\mathrm{i}=1}^{\mathrm{n}}\left[{\left(\left|{\mathrm{P}}_{\mathrm{i}}\text{-}{\mathrm{O}}_{\mathrm{mean}}\right|+\left|{\mathrm{O}}_{\mathrm{i}}\text{-}{\mathrm{O}}_{\mathrm{mean}}\right|\right)}^2\right]}}$	(5)
True Prediction Rate (TPR)	$\mathrm{TPR}={\displaystyle \frac{\mathrm{True}\mathrm{Positives}}{\mathrm{True}\mathrm{Positives}+\mathrm{False}\mathrm{Negatives}}}$	(6)
False Prediction Rate (FPR)	$\mathrm{FPR}={\displaystyle \frac{\mathrm{False}\mathrm{Positives}}{\mathrm{False}\mathrm{Positives}+\mathrm{True}\mathrm{Negatives}}}$	(7)
False Alarm Rate (FAR)	$\mathrm{FAR}={\displaystyle \frac{\mathrm{False}\mathrm{Positives}}{\mathrm{False}\mathrm{Positives}+\mathrm{True}\mathrm{Positives}}}$	(8)
Success Index (SI)	$\mathrm{SI}={\displaystyle \frac{\mathrm{True}\mathrm{Positives}+\mathrm{True}\mathrm{Negatives}}{\mathrm{Total}\mathrm{Predictions}}}$	(9)

where, (O_i) and (P_i) represent the observed and the predicted values respectively, (O_mean) is the mean of the observed values and (n) is the number of observations in each case.

4. Results & Discussion

Table 6 depicts the values of the statistical evaluation indices (MAE, RMSE, R and IA) for the best developed ANN model, for each one of the six air pollutants among the nine examined locations and for all of the eight examined scenarios. According to Table 6, it seems that for particulate matters and NO₂, ANN#5 has the best predictive performance. For SO₂, O₃ and CO, ANN#4 presents the best predictive ability. In all cases, the most suitable scenarios are S2 and S1 (see Table 4). Location 8 seems to have the best forecasting ability, especially for air pollutants NO₂, SO₂, O₃ and CO. This may lead to the conclusion that location 8 could be the base for air pollution forecasting of the other locations. Concerning the general forecasting ability, we can say that the correlation coefficient (R) is lying between 0.911 and 0.954 as well as the index of agreement (IA) is lying between 95.31% and 97.64%. Both of these indicate a very good forecasting ability for the next 24-hours with an hourly forecasting step.

Table 7 shows the values of the exceedance’s statistical evaluation indices (TPR, FPR, FAR and SI) for the best developed ANN model, for each one of the six air pollutants among the nine examined locations and for all of the eight examined scenarios.

Concerning the forecasting of the exceedances, in other words the cases where the concentration of the examined pollutants is greater than a given threshold value based on WHO directives and was forecasted correctly or not, seems that in all cases model ANN#5 gives the best prediction. Also, location 8 seems that can be considered as a reference location in future works. Furthermore, S1 and S2 were found to be again the best training scenarios among the eight examined scenarios. Finally, TPR, which gives the rate of exceedances that observed and correctly forecasted, lying between 88.16% and 97.75% while SI which shows the overall ability of right forecasting of the exceedances is lying between 93.113% and 99.86%. Both, indicate that the developed ANNs models are able to give a very good and sufficient forecasting of the exceedances.

In the effort to be derived the general behavior of the developed ANNs models, in terms of their forecasting ability, appropriate Box & Whisker graphs were created. Necessary data for the design of these graphs are the maximum, average and minimum values of IA (Figure 5) and SI (Figure 6) respectively, concerning all of the developed ANNs, for each air pollutant and for each one of the examined nine locations, within the greater area of Beijing, China. More concretely, data were composed from the best performance values for each pollutant and for the optimal training function, therefore from 72 total values (9 locations X 8 input data training scenarios).

Figure 5 shows that the mean values of IA for all of the developed ANNs models and for all of the forecasted air pollutants is lying between 0.92 and 0.95 indicating an extremely good forecasting performance. In addition, seems that the developed ANNs models are able to forecast next day 24-hours concentrations of SO₂, PM_2.5, CO and O₃ in a more sufficient manner than NO₂ and PM₁₀.

In the same fashion as in Figure 5, but in this case concerning the ability of the developed ANNs to forecast the air pollutants concentration exceedances, seems in Figure 6 that the mean values of SI, for all of the developed ANNs models and for all of the examined air pollutants, is lying between 0.88 and 0.95 indicating an extremely good forecasting performance. In addition, seems that the developed ANNs models are able to forecast the exceedances of next day for SO₂, PM_2.5, CO and O₃ in a more sufficient level than NO₂ and much more than PM₁₀.

5. Conclusions

The aim of this work was to create a universal forecasting model of air pollutants concentrations, specifically PM_2.5 and PM₁₀, as well as SO₂, NO₂, CO and O₃. A basic condition for the training of these models is the appropriate pre-processing of the input data in order to extract any hidden relationships, which will facilitate the subsequent creation of the scenarios. The gap-filling process was an innovation that was not found in any of the forementioned literature and offered satisfactory results. The algorithms created for this process are also universal models, and their application is feasible to any other data set, with minor adjustments. Additionally, the comparison of eight possible input scenarios and the training of each with ten different training functions (ANNs models architecture), was conducted. The results offered valuable insight regarding the optimization of the training of ANNs models having as a constant variable the pollutant of interest. The results were acceptable for the majority of pollutants with average prediction values well above 80.0% accuracy. Through further statistical analysis it was shown that the use of all of the available meteorological variables enhances the training performance of ANNs and does not "confuse" them. It was also observed that the BR₄ (ANN#5) structure is the most suitable. It seems that the exported model can be used by both public and private bodies so as to achieve the immediate information of the former and to assist the latter in protecting themselves from the harmful environmental conditions.

Concluding, the developed ANNs forecasting models shows an operational interest since the forecast can be made at any time during the day, for the next day, giving an advantage in making correct, valid and timely decisions by the competent agencies.

Finally, it is suggested that further research is required in order to improve the prediction of air pollution so that the developed models have an optimal design and performance for public and private authorities’ decision making, aiming the protection of public health and also to avoid adverse health effects, as well as adverse effects on constructions and infrastructures, taking into account the climatic crisis in addition.