In this study, a comprehensive modelling on air pollution was carried out by including all parameters with a holistic approach. For the three inputs studied here, there are seven possible combinations. The corresponding values computed for each PM output were stored and statically compared to determine the best combinations that can provide the considered PM with the best possible accuracy.
All combinations can be expressed as:
- Comb1: Temperature
- Comb2: Pressure
- Comb3: Humidity
- Comb4: Temperature and Pressure
- Comb5: Temperature and Humidity
- Comb6: Pressure and Humidity
- Comb7: Temperature, Pressure and Humidity
First, the prediction capability of each ML model employed in this work for forecasting the PM10 concentrations is checked, then the most appropriate model for each station is selected. In this step, the ML models are compared and ranked based on the performance score 𝜑 and then on the coefficient of determination R² (confidence level is 0.95), MAPE, and σ. These indicators are given with dark blue (for the rank), black, sunshine yellow, and light blue colours, respectively. The results of the comparison are illustrated in Figure 6. Here for each ML model, we have compared the accuracy of all combinations, and have considered only the best one.
As clearly shown, the best accuracy is found to be for the DT model. With this model, the estimates are statistically very significant. The corresponding R² is closer to 1, which indicates perfect correlation and relationships between the measured values and the predicted ones, where other indicators of dispersion are closer to zero. More results can be obtained from the same figure. Compared to what were presented in Table 1, the correlations we found here indicate very accurate prediction and outperformed the results given by the models studied and applied by the corresponding researchers. For example, (Choubin et al., 2020), found an accuracy>87% and a precision > 86% for the hazard prediction of PM10 in Barcelona. Here, the accuracy and the precision found by DT model are close to 98% for almost all stations/sensors studied.
In the next subsections, we will apply the DT model for predicting the PM1, PM2.5, and PM10 concentrations for all studied stations/sensors. For each station/sensor, we will compare the accuracy of all combinations of predictor variables, and then the best one will be selected and considered later in the modelling step. The comparison is always done based on the performance score 𝜑 and then on the coefficient of determination R² (confidence level is 0.95), MAPE, and σ. The rank for each combination will be also shown.
5.1 Correlation between the PM1 and PM2.5, and PM10 concentrations
In Figure 7, the correlation between PM1 and PM2.5, and PM10 is checked by applying the hybrid FS-DT model to the 12 studied stations/sensors. The inputs are PM1 and PM2.5 while the output is PM10. There are three combinations: - Comb1: PM1, - Comb2: PM2.5, and - Comb3: PM1 & PM2.5. It has been noticed that the strong correlations are found to be between PM2.5 and PM10 (close to 0.99) followed by that between PM1 and PM10 (R² is between 0.89 and 0.98). In most cases, using PM1 and PM2.5 as inputs we can highly predict PM10 with most excellent accuracy and greatest precision. The results found here indicate that the PM10 concentrations is effectively related to the PM2.5 and with a bit strongly to the PM1.
5.2 Hybrid FS-DT model applied for forecasting PM1 concentrations
Based on the-state-of-the-art done, no paper was found for forecasting and/modelling the PM1 concentrations. Also, in the WHO recommendations, we cannot find AQI classifications based on the PM1 concentrations. In this work, we have applied hybrid FS-ML models to the hazard PM1 predictions, because we think that this particulate matter also can have a negative impact on human health and the ecosystem.
In Figure 8, all possible combinations of predictor variables studied are checked for forecasting and then modelling the PM1 concentrations for all studied stations/sensors. As shown, for almost all sensors (excluding only sensor 16000209), the pressure is the first important predictor followed by temperature and humidity, respectively. For the sensor 16000209, the temperature is the first important predictor followed by the pressure and humidity, respectively. This maybe because the geographical coordinates of the sensor 16000209 or because the climate characteristics of the sensor location.
The results found here indicate that the humidity has a lower influence on the PM1 concentrations. In general, the R² are between 0.5 and 0.9, between 0.7 and 1, and between 0.4 and 0.7 for temperature, pressure, and humidity, respectively. The best accuracy is discovered by combining pressure to temperature and slightly to humidity. This accuracy is justified by the correlation R² that is between 0.9 and 1 and by the indication of dispersion, the MAPE, and the σ that are closer to zero.
Moreover, excluding sensors 1600020A and 16000238, the best accuracy is shown by combining the pressure to temperature, while for other sensors, the humidity is added to slightly enhance the prediction’s accuracy. The statistical results done indicate almost perfect correlation and approximations between the PM1 values predicted by these two combinations and the measured values. R² is found to be closer to 1 and MAPE and σ to 0. Other results can be extracted from the same figure.
5.3 Hybrid FS-DT model applied for forecasting PM2.5 concentrations
In most articles that have been read, authors have tried to predict PM2.5 and/or PM10 concentrations based on various sets of predictor variables and by employing several machine learning methods. In most cases, correlations found between these objective functions and the predictor variables studied here within this study do not reach the confidence interval 0.95. The readers are referred to references summarized in Table 1 for getting this information. In this study, the correlations we show are found to be closer to 1 (accuracy close to 100%) for almost all stations/sensors studied (see Figure 9).
In Figure 9, all possible combinations of inputs are checked for forecasting the PM2.5 concentrations in all studied stations/sensors. By excluding only sensor 16000209, for all other stations, the pressure is the first significant predictor followed by temperature and humidity, respectively. For the sensor 16000209, the temperature is the first important predictor followed by the pressure and humidity, respectively. This indicates also that the humidity has a lower influence on the PM2.5 concentrations. In addition, for all stations/sensors, the best accuracy is shown by combining the pressure to the temperature and slightly to the humidity.
5.4 Hybrid FS-DT model applied for forecasting PM10 concentrations
The coarse particulate matter PM10, which is known as atmospheric particles with a diameter between 2.5 and 10 µm, has a broad negative impact on human health, mortality level, illness, as well as on the environment and ecosystem (Fortelli et al., 2016). The possible relationship between local meteorological patterns and PM10 air pollution has been widely investigated by researchers worldwide. Several ML models were employed to accurately forecast PM10 using numerous meteorological inputs. This subsection is coming in this context.
Like the above subsections, in Figure 10, all possible combinations of the predictor variables considered here are checked for forecasting the PM10 concentrations at all studied stations/sensors. Like PM1 and PM2.5 concentrations, the pressure is the main significant predictor followed by the temperature and the humidity, respectively. Only for the sensor 16000209, the temperature is the first key predictor followed by the pressure and the humidity, respectively. This is to say that the humidity has smaller influences on the PM10 concentrations. In addition, except for the sensor 1600020F, the best accuracy for all other stations/sensors is observed by combining the pressure to the temperature and a little to the humidity. For the sensor 1600020F, the best accuracy is given only by combining pressure to temperature. This maybe because this sensor is the sole that has registered outstanding Hazardous AQI values (4473 values). These remarks request us to do another study on the possible relationship between the AQI and/ the PM concentrations and the predictor variables studied for each station/sensor and for each AQI category (Good, Moderate, Unhealthy for sensitive groups, Unhealthy, Very unhealthy, and Hazardous categories).
5. 5 Modelling of PMs and AQI
In this subsection, the LSR was applied to establish new relationships between the considered objective function (PM1, PM2.5 or PM10) and the found best combinations of predictor variables. The new formulas built are reported in Table 3 (see the Annex). For the AQI computing, we have applied the formulas adopted by the US-EPA, in which the AQI ranges from 0-500, 0 stands for good environment and 500 for hazard environment. The formulas used here is as given in Eq. (11). Then, we have used the equation two times (for PM2.5 and PM10) and the worst sub index (the max value) communicates the AQI.
$${\text{I}\text{n}\text{d}\text{e}\text{x}}_{\text{p}} = \left[\frac{{{\text{I}\text{H}}_{\text{i}}–\text{I}\text{L}}_{\text{o}} }{{\text{B}\text{P}\text{H}}_{\text{i}}–{\text{B}\text{P}\text{L}}_{\text{o}}}\right]\left(\text{C}\text{p}–{\text{B}\text{P}\text{L}}_{\text{o}}\right)+{\text{I}\text{L}}_{\text{o}}$$
11
Where \({\text{I}\text{n}\text{d}\text{e}\text{x}}_{\text{p}}\) is the index for the pollutant p; Cp is the truncated concentration of the pollutant p; \({\text{B}\text{P}\text{H}}_{\text{i}}\) is the concentration breakpoint i.e., greater than or equal to Cp; \({\text{B}\text{P}\text{L}}_{\text{o}}\) is the concentration breakpoint i.e., less than or equal to Cp; \({\text{I}\text{H}}_{\text{i}}\) is the AQI value related to \({\text{B}\text{P}\text{H}}_{\text{i}}\); \({\text{I}\text{L}}_{\text{o}}\) is the AQI value related to \({\text{B}\text{P}\text{L}}_{\text{o}}\).
Based on the formals developed here for each PM, we have elaborated a new interface that makes easier the prediction of both the PMs and AQI (see Fig. 11). Using this interface for a given sensor/location, we can easily predict the PMs concentrations and then the AQI based on the meteorological variables studied within the study. Using this interface, we may only use the best combination of the predictor variables for each station/sensor to predict the objective functions considered (PM1, PM2.5, PM10, and AQI).
5.6 Correlations between PM10 and Noise and CO2
For the sensor 820002C3, which is the sole sensor that additionally measures noises and CO2 concentrations, the correlations between Noise and CO2, and PM10 were checked. For the Noise, the inputs 1 to 3 were, respectively, Noise min, Noise max, and Noise average. For the CO2, the inputs 1 to 3 were, respectively, CO2 min, CO2 max, and CO2 average. So, there are seven possible combinations for each predictor variable.
As shown in Figure 12, the correlations we found for both the noise data and CO2 data are less than the confidence interval of 0.95, and in the best cases, they are close to 0.85. This indicates that the PM10 concentration is not strongly related to these measured data, and there is a need for other predictor variable that may complete the prediction accuracy. The indicators of dispersion MAPE and σ, in most cases, indicate little worst approximation and precision between the PM10 data and the predictor variables the Noise and the CO2. This indicates that we cannot build relationships between the PM10 concentrations and the Noise and CO2 data. Other remarks can be revealed from the same figure