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Pollutants, the undesired substances, degrade the ecosystem with their adverse effects and cause pollution. When concerned with the imbalance in the atmosphere, this pollution is called air pollution. It kills an estimated seven million every year, with low- and middle-income countries suffering the most (Osseiron and Lindmeier, 2018; WHO, 2018). A significant relationship between atmospheric pollutants and health hazards is reported, and their exposure increases the risk of cardiovascular diseases, fertility issues, and mental health in particular (Chen et al., 2018; Manan et al., 2018; Merklinger-Gruchala et al., 2017; Curtis et al., 2006; Mortimer et al., 2002; Wong et al., 2001). Particulate matter variation studies in India have shown Delhi as the most polluted city when compared to Kolkata, Mumbai, Hyderabad (Singh et al., 2021), with values of PM_2.5 (Particulate matter of 2.5 microns or smaller) and PM₁₀ (Particulate matter of 10 microns or smaller) exceeds National Ambient Air Quality Standards (NAAQs) 60 mg/m³ (Guo et al., 2019). Studies have attributed agricultural fires as one of the reasons for this (Cusworth et al., 2018). Furthermore, the existence of the relationship between the outbreak of COVID-19 and air pollution is also reported (Roy, 2021). Moreover, an increase in levels of NO₂ (Nitrogen dioxide), O₃ (Ozone), and SO₂ (Sulphur dioxide) have potential health concerns (WHO, 2018).

Considering the harmful nature of these pollutants, it is important to monitor these pollutants. However, due to the high cost of placing monitoring instruments everywhere, sometimes the pollutants can be predicted at a non-monitoring site using various available methods. There have been a number of studies around the globe that have predicted these criterion air pollutants using machine learning (Qi et al., 2019; Wen et al., 2019; Yeganeh et al., 2018; Fan et al., 2017; Zou et al., 2015; Papaleonidas and Iliadis, 2013; Rigol et al., 2001) and Regression models (Kerckhoffs et al., 2021; Boaz et al., 2019; Wang and Song, 2018; Alam and McNabola, 2015; Russo and Soares, 2014; Dominick et al., 2012; Crouse et al., 2009).

There have also been some studies, wherin a comparison of various methods to predict these pollutants have been done. The spatial interpolation methods such as geostatistical methods (various kriging methods), local interpolators (Thiessen polygons, IDW, splines), global interpolators (trend surfaces or regression models), and mixed methods were analyzed by Vicente-Serrano et al. (2003). Spatial interpolation methodologies were summarized for urban air pollution modeling based on the application for the greater area of metropolitan Athens, Greece (Deligiorgi and Philippopoulos, 2011). The proposed methodologies include Nearest neighbor method, Triangulated irregular network method, Natural neighbor method, Inverse distance weighting (IDW) method (with linear and squared IDW), Radial basis function (RBF) method, Thin plates splines method, Kriging method, and Artificial neural network (ANN) method. The application of spatial interpolation methods was given to many disciplines (Li and Heap, 2011). A total of 72 spatial interpolation methods were analyzed, and comparative performances were provided in their study by Li and Heap (2014). They included the most frequently used methods as Inverse distance weighting (IDW), ordinary kriging (OK), and ordinary co-kriging (OCK) also. The spatiotemporal prediction at the non-monitoring site was presented by Alimissis et al. (2018) using interpolation methods to determine the air pollution at a new location.

Some previous studies in India focused on the missing data prediction using previous data of pollutants or meteorological data or their combinations as predictors. Singh et al. (2012) provides a comparison of the linear (PLSR) and nonlinear (MPR, MLPN, RBFN, and GRNN) models for urban air quality prediction (RSPM, SO₂, NO₂) using data of temperature, relative humidity, wind speed, SPM, NO₂, and SO₂ data and shown more remarkable performances of GRNN models than the MLPN and RBFN. Nagendra and Khare (2006, 2005) compared among three choices of input data sets for the prediction of NO₂ firstly, using meteorological and traffic data, secondly, using only meteorological data, and lastly using only traffic data. MLR and PCA+ANN models were evaluated with statistical analysis by Mishra and Goyal (2015) for NO₂ forecasting models at Taj Mahal, Agra using NO₂, SO₂, temperature, CO, O₃, RH, WS, and WDI (wind direction index) as predictors. The performances of PCA approaches were found better than the MLR in their analysis. The performance for the MLP model was found better as compared to RBF and GRNN models for all seasons (Kumar et al., 2017).

Thus, the prediction studies of air pollution have been done for a particular location to evaluate the missing data using the pollution data and meteorological data of that location or a combination of both. The studies have also been done to predict air pollution at a location using pollution data of other sites and other predictors. However, the studies predicting the air quality at a new location (other than monitoring site) using spatial interpolation methods have not been done in India.

In this study, the prediction of air quality parameters at a location of a non-monitoring site is presented over Delhi, India. The air pollution data of the neighboring monitoring sites have been used for the predictions of NO₂, O₃, PM₁₀, PM_2.5, and SO₂. The specific objectives of the present study are:

• (i) Prediction of criteria air pollutants (NO₂, O₃, PM₁₀, PM_2.5, and SO₂) at non-monitoring sites in Delhi using five different methods (average method, best correlation coefficient method, weighted average, inverse distance weighting method, and grid interpolation method).
• (ii) To compare the performance of these five methods on the basis of prediction efficiency.

The present study is conducted for Delhi, India; located between 28.42°N to 29.00°N latitude and 76.86°E to 77.36°E longitude (Fig. 1). Delhi is one of the major cities in India, with rapid growth in population, traffic, industrialization and construction activities. This has led to higher energy consumption. Moreover, the availability of alternate energy sources is limited, thus further increasing the air pollution in Delhi. The air quality observation data for the study area is obtained from CPCB (Central Pollution Control Board of India) at ‘https://app.cpcbccr.com/AQI_India/’, and the same is also provided at ‘https://openaq.org/’. Table 1 shows the statistical summary of fifteen minutes scaled dataset of the five pollutants (PM_2.5, PM₁₀, NO₂, SO₂, and O₃) for the 46 stations over Delhi in the period of January 1, 2018, to October 30, 2020.

Fig. 1. 
The location of Delhi (the capital) in India showing 19 observation stations and 6 test stations.

Analysis showed that, only 25 of these stations had missing data less than 75%, which were used for prediction and validation. The top six monitoring stations (Table 2) having maximum missing data out of the 25-monitoring station was reserved for validation, while the remaining 19 monitoring station with the lowest missing percentage was used for prediction model development purposes (Table 3).

In this study five different methods (Simple Averaging, Best Correlation Coefficient Method, Weighted Average Method, Inverse Distance Weighting method, and Grid Interpolation Method) have been evaluated in terms of prediction efficiency. Theses are the methods which are commonly used in the previous studies (Jin et al., 2011). The correlation analysis was performed to check the dependency among the chosen monitoring stations. The correlation analysis was performed between 19 monitoring stations using the entire data at 15 min intervals at seasonal (Winter: January and February), Summer: March, April, and May, Monsoon: June to September, and Post-monsoon period: October to December) and annual scales.

The increasing availability of historical data, the number of monitoring stations, and computing resources have facilitated us to develop more advanced models for air pollution prediction. In this study, a methodological comparison to predict the mass concentration of NO₂, O₃, PM₁₀, PM_2.5, and SO₂ at any non-monitoring site was carried out.

A correlation analysis was done to check the interdependency of pollutants concentration data among the different observation stations. The correlation matrix was calculated based on the pollutant’s concentration data of three years. Further, a model is established based on the correlation coefficients between any pair, their distance, and the direction of the line joining among the 19 monitoring stations of Delhi. This model predicts the strength of correlation between non-monitoring sites and 19 monitoring stations of Delhi.

Five different methods were adopted to predict mass concentrations at non-monitoring sites using the mass concentration data of those monitoring sites, showing a good correlation with non-monitoring sites. Six additional monitoring stations’ mass concentrations data were used to validate predicted mass concentrations at those sites. The percentage errors and RMSE were calculated, and comparison was carried out among the methodologies in different seasons for each pollutant.

The correlation between the two monitoring stations has no relation with the direction of their spatial position (direction of the line joining them). The results showed that a simple average on the dependent station model performed best over other methods. The performance of the proposed method is also consistent both for optimal prediction at all stations and has the second minimum mode RMSE among different prediction methods. These methods can be used in future studies and other regions for air pollutant prediction.

The conclusions of the present study can be enumerated as:

• 1) Based on the correlation analysis, we found that the stations showed higher correlations for the Particulate matter (PM_2.5 and PM₁₀) compared to other pollutants.
• 2) Overall, the Grid interpolation method with dependent station was found the best (lowest median RMSE=5,107.5 μg/m³) whereas the Weighted Average was the worst (maximum RMSE=9,734.9 μg/m³).
• 3) Averaging is found to be the best prediction method based on mode RMSE(=18.85 μg/m³), whereas the Best correlation coefficient method was found to be the worst prediction method (mode RMSE 41.60 μg/m³).
• 4) Overall, the prediction for SO₂ was the best among all the pollutants whereas for O₃, it was the worst. Considering different seasons, it was easier to predict the pollutants in the monsoon season, whereas it was most difficult in the post monsoon season. This can be attributed to corresponding level of pollution in these seasons.
• 5) The methods that used dependent station data (Average, IDW, and GI DS) always have greater mode R², whereas the methods that used all station data (BCC, WA, and GI AS) always have mode R² smaller as 0.1 (Fig. 15).

One of the major limitations of this study is the lack of available information about point source pollution. If emission data about these major point sources were available, proper weights could be assigned to these stations based on distance and direction from the source of pollution. Moreover, the distances between the stations is small, therefore the outcomes of the study may be limited only up to the spatial extent of the study area.