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Over the past years, airborne particulate matter (PM) concentrations in Indian cities have been rising and became a matter of concern for the policymakers in India. The effort towards air quality improvement is not easy for a country like India as the country policymakers cannot forego the objective of faster economic development to sustain its vast population. Different sources are continuously pouring pollutants in the city air, and notable amongst them are burning of fuels, industrial establishments, different constructions related to infrastructure, power plants both government and privately operated, stubble burning of agricultural biomass residue in the neighborhoods, and vehicular movements (Guttikunda, 2017). However, their proportional contribution varies across the cities of India. If the whole of India is to be considered about 53,929 automobiles hit India’s road every day (Dutta and Dutta, 2018). All led to the dismal status of air pollution situation across the cities of India. Table 1 and Table S1 present a summary of studies conducted by different researchers in the context of 28 Indian cities with reported level of PM₁₀ concentrations and times they violated the air quality standard of both World Health Organization (WHO) and National Ambient Air Quality Standards (NAAQS) of India, respectively. Kolkata, a tier-1 city^* in India, even clocked PM₁₀ concentration of as high as 445±21 μg m^-3 during the wintertime (Das et al., 2015). Annual PM₁₀ concentrations in New Delhi were reported to be 222±14 μg m^-3 while an earlier study reported summer and winter mean concentrations as 95.1±22.2 μg m^-3 and 182±32.5 μg m^-3, respectively (Tiwari et al., 2014; Singh et al., 2011). Bengaluru city also registered a high annual mean PM₁₀ concentration level of 349.8±205.8 μg m^-3 during the year 2015 (Guttikunda et al., 2019). In comparison, lower concentrations have been reported for Hyderabad and Mumbai where mean PM₁₀ concentrations for the period 2005-2012 were 174.4±86.6 μg m^-3 and 54.4±25.2 μg m^-3, respectively (Dholakia et al., 2014).

The tier-II cities are also not lagging far behind the India’s tier-I cities in terms of PM₁₀ pollution. Raipur had mean PM₁₀ concentrations of 387.29±76.9 μg m^-3 during October 2008 to September 2009 while another city Kanpur recorded mean PM₁₀ concentrations of 277± 117.6 μg m^-3 during October 2002 to February 2003 (Deshmukh et al., 2011; Sharma and Maloo, 2005). Amongst the tier-III cities, the reported mean PM₁₀ concentrations of some specific cities like Jharia and Sonipat were also on the higher side with 333.7±17.9 μg m^-3 and 213.7±151.5 μg m^-3 during the period March 2011 to February 2012 and 03 December to 06 December 2016, respectively (Ravindra et al., 2019; Roy et al., 2019).

One option to the Indian policymakers to mitigate critical PM concentrations in the cities, vis a vis health effects, therefore, may be to correctly predict the concentrations at least one to two days in advance and accordingly initiate prior actions such as regulation of traffic in a planned way. However, predicting the air quality is not so straightforward job because of the complex interactions of different nonlinear parameters (Hooyberghs et al., 2005). Shahraiyni and Sodoudi (2016) reviewed 36 research studies executed in different cities of the world in the quest of achieving prediction accuracy in forecasting PM₁₀. In these studies, 50% of researchers employed a multi-layer perceptron (MLP) with Feedforward Backpropagation Network (FFBN) topologies, a class of Artificial Neural Network (ANN) model. Around 28% (10 studies) depended on the widely used Multiple Linear Regression (MLR) technique for PM₁₀ forecasting in urban areas. Three studies (about 8%) used the Radial Basis Function (RBF) network of ANN class to forecast city-level PM₁₀. The other five studies (14%) depended on different other techniques like PNN (Pruned Neural Networks), LL (Lazy Learning), MLP and MLR combo, Elman class of Recurrent Neural Networks (RNN), and PCRA (Principal Component Regression Analysis). ANN technique appears to be providing useful results to deal with nonlinear independent variables involved in environmental pollution prediction. Hence, more practitioners resort to ANN modeling type of data-driven approaches as alternatives to traditional deterministic or nonlinear models (Cabaneros et al., 2019; Jiang et al., 2017). Pollution researchers of China and elsewhere have used ANN techniques extensively to forecast airborne PM concentrations in the past. The use of MLR with stepwise inclusion of input variables has been the most used tool for temporal prediction of PM_2.5 and PM₁₀ in different urban areas of India. MLR has its limitation in terms of the linear representation of nonlinear systems. However, researchers have, in a limited way only, showed a preference for different data-driven predictive techniques for PM forecasting in the Indian context and comparatively judge their performances (Table S2).

Against the above background, this paper’s primary objective is to assess the predictive ability of three contemporary statistical techniques namely MLR, ANN, and CART (Classification and Regression Tree) analyses for one day ahead PM₁₀ concentration prediction of an Indian city. The best-performed technique will be a useful tool for city authorities and air quality managers for initiating in situ measures to curb pollution. Unlike previous modeling efforts (Table S2), this is the first instance concerning applying CART analysis as a statistical procedure for the prediction of PM₁₀ in a comparative set up of an Indian city. In the recent past, Gocheva-Ilieva and Stoimenova (2018) employed CART in predicting PM₁₀ for the Pleven city of Bulgaria and claimed very accurate model performance. The CART technique as a method for analysis and forecasting of PM₁₀ claimed to have performed better than MLR (Slini et al., 2006).

The model development for forecasting PM₁₀ was attempted in the north-eastern Indian tier-II city of Guwahati, capital city of the state of Assam, India. For the last 10-12 years, Guwahati has been recognized as one of India’s most rapidly growing cities. Rapid urbanization and its contribution to air pollution have made smaller Indian cities like Guwahati vulnerable too. Vehicular growth (both light and heavy vehicles) in the city was notable in the past decade, with about a reported sharp rise of 87%. A recent study conducted in Guwahati, computed Hazard Quotient (HQ) based on NAAQS and WHO, indicated quite a high degree of health risk for the city dwellers (Dutta and Jinsart, 2020). There is black carbon pollution in the city air due to rapid urbanization and poor environmental quality control (Barman and Gokhale, 2019). Guwahati has a humid subtropical climate. The four major seasons of the city are winter (December to February), spring (March to May), summer ( June to August), and autumn (September to November), with differing meteorological conditions. Guwahati has six ambient air monitoring stations, set up under the National Air Quality Monitoring Programme (NAMP), to measure key pollutants (Pant et al., 2019). Only one of the NAMP stations can measure PM_2.5, while the newly developed CAAQM (Continuous Ambient Air Quality Monitoring) station started functioning only during mid of 2019. The six NAMP stations’ location and their monitoring type in the backdrop of Guwahati city can be seen in Fig. 1 and Table S3, respectively below.

Fig. 1. 
Study location and monitoring stations.

Daily average concentration data (1096 data points) for PM₁₀ (μg m^-3), CO (ppm), NO₂ (ppb), and SO₂ (ppb) were collected in respect of all the six air quality monitoring stations for three years 2016-2018 from State Pollution Control Board (SPCB) office located at Guwahati. The three years (2016-2018) daily climate data (1096 data points) for ambient temperature (AT, °C), relative humidity (RH, %), wind speed (WS, ms^-1), rainfall (RF, millimeter) were acquired from Regional Meteorological Department, located at Guwahati.

3. 3 Predictive Models Development and Validation

We have used MLR analysis, MLP class of ANN, and CART for forecasting of one day ahead PM₁₀ concentration for all the six air quality monitoring stations of Guwahati city.

3. 3. 1 Multiple Linear Regression (MLR)

In MLR analysis, the mathematical model was built up to forecast the dependent variable, i.e., next day PM₁₀ based on the inputs of independent variables comprising of climate variables and gaseous elements. In MLR, the coefficient of determination (R²) indicates the overall capability of the model to handle variance in data. The regression model was composed following equation 1 (Abdullah et al., 2019; Vlachogianni et al., 2011).

Yi=β0+β1X1i+β2X2i+⋯+βnXni+εi

(1)

where Y is the dependent variable, β_i is the regression coefficients, X_i is the independent variables and ε is a stochastic error associated with the regression. This relationship was used in this study to develop a mathematical equation model to predict the next day PM₁₀ concentrations of the six ambient air monitoring stations of Guwahati with input variables like meteorological parameters, PM₁₀, and gaseous pollutants. MLR assumes that the residuals have a normal distribution with a zero mean, uncorrelated and constant variance. The stepwise multiple linear regression procedure was used here to derive the mathematical equation (Abdullah et al., 2019). Variance inflation (VIF) was used in this study to evaluate the multicollinearity effect on the variance of the estimated regression coefficient. The equation for VIF (Equation 2) is as follows:

VIF=11-R2

(2)

3. 3. 2 Multi-Layer Perceptron (MLP) Model

ANN is a robust data modeling technique capable of handling the nonlinear relationship between variables and hence found suitable for the prediction of PM₁₀ which requires exploration of the complex relationship between particulate matters, meteorological variables, and gaseous pollutants present in the atmosphere (Feng et al., 2015). We have used MLP in this study to create predictive models for each of six ambient monitoring stations of Guwahati using nonlinear combinations of the input variables (meteorological parameters, PM₁₀, PM_2.5, and gaseous pollutants) to predict the next day PM₁₀ concentrations. MLP forms a network of functionally interconnected neurons, also known as perceptron (Vemuri, 1988). ANN scores more than MLR because of its ability to predict the dependent variable of a builtup model more accurately (Gardner and Dorling, 1998). MLP has a simple structure consisting of three layers: the input layer, hidden layer, and output layer. One hidden layer was considered in our study, as it was suggested to be sufficient to achieve the optimum model capacity (Bishop, 1995). The number of neurons or the nodes, in the input layer, was equal to the number of input variables introduced in the model. The relevant input variables, i.e., observed meteorological parameters, PM₁₀, and gaseous pollutants, are fed in the model as signals to the input layer of the model, which is then passed on to the hidden layer. The neurons do the computations to detect features of the input variables and introduce them to the input layer with requisite weights. The weights are assigned to input variables based on their relative importance. The hidden layer does the critical function of nonlinear transformations of the inputs entered the network through a predefined activation function. The neuron sums up information, including bias, in the hidden layer. The bias does the job of providing a trainable constant value to every neuron in addition to its normal value. The mathematical formulation of the MLP model is as shown below in equation 3:

Y=F∑j=1mWkj∙F∑i=1nWjiXi+Bj+Bk

(3)

where Y=output, F=transfer function, W_kj.=weights between hidden and output layers, W_ji=weights between input and hidden layers, X_i=input variables, m=number of neurons in a hidden layer, n=number of neurons in an input layer, B_j=bias values of the neurons in the hidden, and B_k=bias values of the neurons in the output layers. Fig. 2 depicts the basic structure of the MLP framework.

Fig. 2. 
The architecture of the MLP network.

3. 3. 3 Classification and Regression Trees (CART)

CART is a non-parametric regression technique that can be employed for the prediction of an independent variable when the distribution of independents variables is not known. Typically, therefore, the CART method tries to ascertain the distribution pattern of the outcome (dependent) variable using the independent variables through their linear or nonlinear relationship with the outcome variable. CART builds up a decision tree through a hierarchy of binary decisions. Each binary decision will involve splitting a target variable into two alternative and mutually exclusive branches (groups) depending upon the variation/values of the explanatory variable leading to the most considerable possible reduction in post-split variations/values of the target variable. In other words, splitting stops when there is no additional gain by further splitting can be achieved (Mckenney and Pedlar, 2003; Moisen and Frescino, 2002). Predictive CART models have been built up in this study for each of the ambient air quality monitoring stations with observed independent predictor variables like meteorological parameters, PM₁₀, and gaseous pollutants of the respective stations to predict the respective dependent variables i.e., next day PM₁₀ concentrations of the city.

3. 3. 4 Model Validation

MLR, MLP, and CART equations have been validated by computing net absolute error (NAE), mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), index of agreement (IA), coefficient of determination (R²) (Grzesiak and Zaborski, 2012; Jinsart et al., 2010; Willmott et al., 2009). Table 2 provides the performance indicators for model validation.

Table 2. 
Performance indicators for model validation.

Sl. No.	Performance indicators	Equations
1	Net absolute error	NAE=∑i=1nPi-Oi∑i=1nOi
2	Mean absolute error	MAE=1n∑i-1nPi-Oi
3	Mean square error	MSE=∑i=0nPi-Oi2n
4	Root mean square error	RMSE=∑i=1nPi-Oi2n
5	Index of agreement	IA=1-∑i=1nPi-Oi2∑i=1nPi-O¯+Oi-O¯2
6	Coefficient of determination	R2=1-∑i=1nOi-Pi2∑i=1nOi-O¯2

SPSS 25 has been used for computation of MLR and MLP while computation for CART SPSS modeler 18 has been used in this study.

The comprehensive and comparative review of PM₁₀ concentration status of 28 different categories of Indian cities (tier-I, tier-II, and tier-III cities) and alarming levels of PM₁₀ concentrations thereof indicate the urgent need to improve city-level air quality. Kolkata, a tier-I city in India, even clocked PM₁₀ concentration of as high as 445±21 μg m^-3 during the wintertime. The tier-III cities like Raipur and Kanpur were found to be not lagging far behind the tier-I cities in terms of ambient PM₁₀ concentration. Interestingly, tier-III cities like Jharia and Sonipat were also recoded PM₁₀ concentration as high as 333.7±17.86 μg m^-3 and 213.67±151.49 μg m^-3 respectively. The PM₁₀ concentrations level in all the 28 indian cities grossly violated both WHO and NAAQS standards by a wide margin. Kolkata topped the list with 22.25 times more than the WHO standard and 7.42 times NAAQS followed by Bengaluru (17.49 times WHO standard and 5.83 times NAAQS), and Delhi (11.1 times WHO standard and 3.7 times NAAQS). Therefore, it is high time for the initiation of some requisite actions for diminishing or preventing the build-up of the high ambient PM₁₀ concentration level in the cities. One way out is abatement action through short term traffic reduction in cities based on predicted PM₁₀ concentration level in advance. Therefore, it entails correct prediction of the city level PM₁₀ concentrations at least one or two days in advance by the local air quality managers through analysis of data routinely gathered by city authorities and predictive modeling thereof.

The tier-II city Guwahati recorded high variability in the observed in PM₁₀ level due to the rapid urbanization. The highest daily average PM₁₀ recorded was 259.39 μg m^-3, while the lowest was 40.67 μg m^-3 during the period 2016-2018. The mean PM₁₀ concentration for the city of 133.22 μg m^-3, as found in this study, violated WHO standard by 6.66 times and NAAQS by 2.22 times which were 4.54 times and 1.51 times respectively, during 2013-2014 (Table 1, Table S1). The average daily NO₂, CO, and SO₂ concentrations of Guwahati were found to be in correlation with PM₁₀ concentrations during 2016-2018 and thereby suggesting a common source for these compounds.

In different cities of the world, different predictive modeling techniques have been used to predict PM₁₀ in advance. However, the use of MLR with stepwise inclusion of input variable was found to be the most widely used tool for temporal prediction of PM₁₀ in different urban areas of India, and that too mostly applied in bigger cities of the country (Table S2). This study found that the next day’s PM₁₀ concentrations, in a tier-II city Guwahati, can be better forecasted using non-linear algorithm MLP with FFBN topologies of ANN class in comparison to linear MLR and non-linear CART model. These three models were critically assessed through a comparative evaluation of performance indicators keeping in mind the end goal is to choose the best-fitted model for accurate forecasting PM₁₀ at the city level. The result of the study reveals that the one day ahead PM₁₀ for all the six-air quality monitoring stations of Guwahati, prediction ability has been relatively better using MLP methods (R²=0. 0.64-0.69; IA=0.88-0.95) and with smallest errors (NAE=0.15-0.22; MAE=16-26.11; MSE=497.86-1408.45; and RMSE=22.31-37.53 in comparison to its closest performer MLR method (R²=0.61-0.68; IA=0.87-0.90; NAE=0.20-0.23; MAE=21.37-26.26; MSE=859.23-1461.48; and RMSE=29.31-38.23). It is interesting to note that CART as predictive method for one day ahead PM₁₀ were close to MLR but not equal in terms of model evaluation indicators with R²=0.52-0.63; IA=0.84-0.88; NAE =0.21-0.26; MAE =21.97-27.35; MSE = 922.12-1700.95; and RMSE=30.37-41.24. The relatively low R² value is quite common in the case of time series dependent nonlinear atmospheric variables with their known confounding effects.

An attempt was made to further validate the predictive performance of the MLP model with respect to the observed PM₁₀ data of the (STN6_193) NAMP monitoring station of Guwahati beyond the period of collected data ( January-March, 2019) used in developing the MLP model. The predicted PM₁₀ concentrations obtained using MLP model have been matched with the same period’s actual data. Fig. S4 shows that the MLP model performed well for the post-study period as well and the model performance indicators (R²=0.69, IA=0.89, NAE=0.07, MAE=13.02, MSE=287.95 and RMSE=16.97) were also in line with the original model (Table S5).

In the backdrop of CPCB’s acknowledgment that comparatively smaller tier-II cities are also facing severe air pollution, city authorities are contemplating initiating several steps for curtailing air pollution and health hazards thereof. We recommend the local authority to use the non-linear algorithm MLP (ANN) with FFBN topologies for forecasting PM₁₀ concentration in the smaller Indian cities like Guwahati too for avoiding PMinduced health hazards to a great extent. ‘Predict pollution and defeat concentration’ could be another approach to fight the air pollution menace in addition to the odd-even rule, which few Indian cities are enforcing presently to rein on air pollution through curtailment of vehicular pollution. The advance prediction approach seems to be more applicable to Guwahati city as this study found PM₁₀ concentration built up had a positive correlation with gaseous pollutants and hence likely to have a common source, i.e., vehicular pollution. Moreover, with this model, the local SPCB authorities can caution city dwellers of impending dangerous levels of PM₁₀, so that they can lessen their outdoor activities for those days and thereby avoiding exposure to unhealthy levels of air quality.