Extreme Events of Reactive Ambient Air Pollutants and their Distribution Pattern at Urban Hotspots

The occurrence of extreme events of air pollutant concentrations at urban hotspots is a routine phenomenon, particularly during the winter season. However, extreme events of reactive air pollutants are more frequent during the summer season. The assessment of air pollution extreme events will provide a platform to formulate an effective and efficient hotspot urban air quality management plan. The statistical distribution model (SDM) is widely used to describe the average as well as extreme air pollutant concentration in a more organized and efficient manner. In the present study, the best fit SDM has been evaluated for hourly average PM2.5 and NO2 concentrations at one of the busiest traffic intersections in Delhi city (air pollution hotspot 1: APH-1) and for PM2.5 at one of the heavily trafficked road corridors in Chennai city (air pollution hotspot 2: APH -2). The SDMs were developed for different seasons to evaluate the impacts of climatic conditions on the air pollution events. Results indicate that NO2 concentrations were best fitted with lognormal and log logistic distribution models respectively, for winter and summer seasons at APH-1. However, lognormal distribution was best fitted to PM2.5 concentration of winter and summer seasons at both APHs.


INTRODUCTION
Urban air pollution (UAP) is a major concern in both developed and developing countries.The sudden rise in vehicle exhaust emissions during peak traffic hour results into extreme air pollution events (episodic conditions) at urban hotspots (Chelani, 2013;Pant et al., 2015).The air pollution episodes are typically occurs during winter periods, characterized by low wind speeds, low mixing heights and temperature inversions (Gokhale and Khare, 2007a;Tiwari et al., 2012).The geography at hotspots in urban regions, especially traffic intersections and congested road surrounded by high rise buildings are leading to sudden occurrences of extreme air pollution events.The urban hotspots are severely prone to vehicular pollution, because of reduced vehicle speed due to traffic congestion and the release of more exhaust emissions (Pant and Harrison, 2013;Gulia et al., 2015).Although, summer condition is favorable for air pollutant dispersion, chemically reactive air pollutants such as oxides of nitrogen (NO x ), secondary particulate matter, having an aerodynamic diameter ≤ 2.5 (PM 2.5 ) and ozone are found to be higher during this season.Kumar et al. (2015) reported that maximum hourly O 3 and NO 2 concentrations of 138.4,µg m -3 , 106.6 µg m -3 and 92.1 µg m -3 during summer, winter and autumn, respectively at one of the urban locations in Delhi city.Chelani (2013) has observed that 24 hour average NO 2 concentration during summer as 116 µg m -3 at one of the traffic location in Delhi city.Pant et al. (2015) have found that 12 hour average PM 2.5 concentration was observed to be 58.2 ± 35.0 µg m -3 with a maximum of 179.5 µg m -3 at an urban hotspot in Delhi city which exceeded the NAAQS value of 60 µg m -3 .However, DPCC (2016) has reported that 24 hour average PM 2.5 is around 300 µg m -3 in Delhi city during summer season.Higher concentrations of these reactive air pollutants during summer season may be due to the chemical transformation of secondary air pollutants, which is significantly influenced by the presence of their pre-cursor pollutants and favorable climatic conditions i.e., humidity and ambient temperature (Wang et al., 2016).The uncertainty in defining the complex behavior of chemically reactive air pollutants in the atmosphere and occurrence of their extreme concentrations can create difficulties in assessment and prediction of air pollution load on shorter time scale (Moussiopoulos et al., 2005;Sharma et al., 2013a).
The statistical distribution model (SDM) can describe air pollutant concentrations in a more organized and efficient manner including extreme as well as average concentrations.
In addition, SDM is a tool of summarizing the information contained in the entire data set in a concise manner (Lu, 2002).In the last two decades, several frequency distribution models were evaluated to satisfy the objectives of the urban air quality management (Taylor et al., 1986;Jakeman et al., 1988;Gokhale and Khare, 2004;Sharma et al., 2013b).These are probability-based models capable of estimating the entire range of pollutant concentration distribution.The SDMs are non-causal and only the monitored air pollutant concentrations are used to develop the models.The distribution form of any pollutants can be influenced by their nature (reactive or non-reactive) and source type (point, area and line), averaging time (1 hour, 3 hour, 24 hour, weekly, seasonal and annual average), emission variation pattern (continuous or discontinuous) and prevailing meteorology (seasonal variations).SDMs can easily describe that how these values of a random variable can spread out over its range.Rumberg et al. (2001) reported that the 3-parameters lognormal distribution model was better represented the PM 2.5 and PM 8.0 concentration data.Chung and Fang (2002) used three theoretical distributions, namely, Lognormal, Weibull, and type V Pearson to fit the measured PM 2.5 , PM 10 and wind speed data.They found that the lognormal distribution model performed best.Gokhale and Khare (2004) reviewed the common methodologies used in statistical distribution modeling.Kan and Chen (2004) used four types of theoretic distributions (Lognormal, Gamma, Pearson V and Extreme value) to fit daily average concentration data of PM 10 , SO 2 and NO 2 and found that the best-fit distributions for PM 10 , SO 2 and NO 2 concentrations in Shanghai were lognormal, Pearson V, and extreme value distributions, respectively.Further, Giavis et al. (2009) found that out of lognormal, gamma and Weibull, only first one is the most appropriate to represent the PM 10 distribution, while the Weibull distribution is unsuitable for this case.Papanastasiou and Melas (2010) verified that the PM 10 concentration distribution can be adequately simulated by lognormal distribution.The probability density function (pdf) of lognormal distribution is capable to predict the number of days when the European Union (EU) air quality standards are exceeded in Volos area.In the recent past, Sharma et al. (2013b) provided an integrated statistical approach for evaluating the exceedences of four criteria pollutants (i.e., SO 2 , NO 2 , CO and PM 10 ) for Delhi mega city and concluded that pdf is a basic and essential tool for realistically evaluating the compliance of NAAQS.Table 1 summarizes some of the past studies on fitting SDMs for air quality data by comparing the types of pollutant, times average concentration and source types.However, most of them are carried for 24 hour average pollutant concentrations and for source specific and did not include PM 2.5 which is one of the critical air pollutants for health point of view.Therefore, the present study is an attempt to evaluate distribution patterns of hourly average PM 2.5 and NO 2 concentrations at two different urban hotspots having different emission, meteorology and geometrical characteristics.Further, extreme event of these pollutants have been predicted and validated with observed concentrations.

EXTREME AIR POLLUTION EVENT AT DESIGNATED AREA IN MEGACITIES
Swelling urban population and increased volume of motorized traffic in cities have resulted in severe air pollution affecting the surrounding environment and human health.In developed countries, national annual average ambient air pollution levels decrease due to implementation of advanced and efficient management practices (Parrish et al., 2011;EEA, 2013).However, the problem of sudden occurrence of extreme air pollution events (episode) still persists.Moussiopoulos et al. (2005) reported that ambient air pollution levels at urban hotspot in twenty European cities were exceeded the specified NAAQS.In the UK, out of total declared air quality management areas (AQMAs), 33% were declared due to exceedance of specified NO x and 21% were due to exceedances of the specified PM standard (Faulkner and Russell, 2010).In European countries, the emission reductions from 1990 to 2009 has been reported to be around 54% for SO 2 , 27% for NO x , 16% for PM 10 and 21% for PM 2.5 .In spite of all these efforts in place, it observed that 18% to 49% of the population in these countries is still exposed to high levels of PM concentration (EEA, 2013).In megacities of North America namely Los Angeles, New York, and Mexico City showed declining trends in some of the criteria air pollutant concentrations Urban area during the last five decades.However, at some designated non-attainment areas (NAAs), the concentrations of NO x and PM 2.5 were found to be violating NAAQS (Parrish et al., 2011;USEPA, 2012).In the Asian subcontinent, few developed countries, e.g., Singapore, Japan and Hong Kong, are also facing street-level air pollution problems due to an increase in the number of motorized transport (Edesess, 2011).In developing countries, all most all mega cities are facing acute air pollution problems i.e., high levels of ambient PM and NO 2 concentrations due to rapid urbanization.In Shanghai, New Delhi, Mumbai, Guangzhou, Chongquing, Calcutta, Beijing and Bangkok, the ambient PM and NO 2 concentrations were frequently violated WHO values (CAI-Asia, 2010).In Beijing, 90% of time, PM concentrations exceed the NAAQS and WHO-AQG (Zhang et al., 2016).In Indian metropolitan cities (Delhi, Mumbai, Kolkata and Chennai), ambient PM concentrations frequently violate the NAAQS as well as WHO guidelines (Guttikunda and Gurjar, 2012;Pant et al., 2015).Recently, studies carried out by Yale University, USA, and WHO, have ranked Delhi as the "worst" polluted city based on an environmental performance index (Hsu and Zomer, 2014).It was observed that increase in vehicular activity as resulted in deterioration of urban air quality in both developed and developing countries (Miller et al., 2006;Ravindra et al., 2015;Wei et al., 2016).

MATERIALS AND METHODOLOGY
Air pollutant concentration is a random variable which can be described accurately using SDM.Initially, NO 2 and PM 2.5 concentrations data were summarized and analyzed in form of descriptive statistics.These statistics provided preliminary assessment on the best fit distribution form of NO 2 and PM 2.5 .The methodology for identification of the best fit distribution model was completed in three steps-(i) selection of the appropriate statistical distribution models, (ii) identification of the best fit distribution model using goodness of fit test and (iii) estimation of the associated model parameters.Based on literature, it was found that air pollutant concentrations are described by continuous distribution models such as Normal, Lognormal, Exponential, Logistic, Log-logistic, Weibull and Gamma (Taylor et al., 1986;Jakeman et al., 1988;Gokhale and Khare, 2007b;Sharma et al., 2013b).Therefore, these SDMs were verified using three goodness of fit tests, i.e., Kolmogorov-Smirnov (KS), Anderson -Darling (AD) and Chi-square to identify the best fit (Taylor et al., 1986;Gokhale and Khare, 2007b).The KS test is found more satisfactory to check the fitting of statistical distributional form of the chemical species (Kalpasanov and Kurchatova, 1976).However, AD test is found more sensitive in calculating the extreme values of concentrations towards the tail (Gokhale and Khare, 2007b).The Chi-square test is commonly used to verify the fitting of SDM with monitored concentration data.The maximum likelihood estimation (MLE) method was used to estimate the associated parameters of the best fit SDM (Ott and Mage, 1976).Further, best fit SDM is used to predict the exceedance of NO 2 and PM 2.5 over specified standard.

I.T.O. Intersection, Delhi City, APH-1
Delhi is one of the seventeen declared NAAs in India (CPCB, 2006) and having population of 22.2 million.It is located at an altitude ~215 m above mean sea level (Fig. 1) and faces heavy seasonal climatic variability.For example, temperature varies from minimum of 4-5°C during the winter (months of December-February) to maximum of 45-48°C during the summer (months of March-May) (IMD, 2010;Perrino et al., 2011).The winter season faces frequent ground based inversion conditions which restrict the dispersion of pollutants.Further, the monsoon season experiences more than 80% of the annual rainfall.In Delhi city, ITO intersection is selected as study site (Air Pollution Hotspot; APH-1).It is one of the busiest traffic intersections in Delhi, located at 28°37'39.70"Nand 77°14'28.60"Eand surrounded by densely populated commercial and residential areas.Based on dispersion modelling and monitored data, numerous studies in past (Khare et al., 2012;Kaushar et al., 2013;Sharma et al., 2014;Kumar et al., 2015;Pant et al., 2015) reported the frequent violations of NAAQS at different urban hotspots in Delhi city including ITO intersections.

Sardar Patel Road, Chennai City, APH-2
Chennai is also one of the seventeen declared NAAs in India, notified by CPCB (CPCB, 2006).It has a population of 4.6 million and located on the South East coast of India at an average altitude of six meters above mean sea level (Fig. 1).In the summer, the city experiences humid weather and strong wind with mean daily temperature reaching 36 ± 2°C.The climatic conditions are strongly affected through formation of land breeze (08:00-11:00) and sea breeze (12:00-14:00).Sea breeze controls the temperature and reduces the mixing height during afternoon, resulting in to poor dispersion of air pollutant.During winter, the ambient temperature reaches 21 ± 2°C.The monsoon experiences 90% of annual rainfall (Sivaramasundaram and Muthusubramanian, 2010).The Sardar Patel (SP) road is selected as a study site (APH-2).It is one of the busiest road corridors in the city, located at 13°00'23.94"Nand 80°14'28.64"Eand surrounded by densely populated institutional and residential areas.The traffic density is varied between 0.17 and 0.14 million vehicles per day, during weekdays and weekends, respectively.Ambient air quality at APH-2 was frequently reported to exceed the NAAQS (Srimuruganandam and Nagendra, 2011;Nagendra et al., 2012).

AIR POLLUTION MONITORING DATA
One-hour average ambient NO 2 and PM 2.5 concentrations data for winter (December 2009-February 2010) and summer (March-May 2010) seasons of the year 2010 were collected from the ambient monitoring station located at APH-1 operated by the Central Pollution Control Board (CPCB), New Delhi.However, missing hours were present in this continuous hourly data due to malfunctioning of the instruments.During winter, hourly PM 2.5 concentrations data were available for one week period only.The APH-1 monitoring station houses laser based particulate monitor which continually collects the data on PM 2.5 and NO 2 taking into account the effects of rains, dust storms or any other meteorological/ weather reverberations, if any.It is observed that out of total number of study hours (i.e., 2184) during the winter season, only 16 no. of hours was affected by the rain, however no dust storm was reported during the winter season.Only NO 2 concentrations were measured during the rainy hours at this station.The percentage of monitoring hours during rain and dust storm for NO 2 and PM 2.5 were 0.7% and 0%, respectively.However, in the summer season, out of total hours (i.e., 2184), only 31 no. of hours, rain were observed.Out of these hours, monitoring were carried out only for 26 and 14 no. of hours for NO 2 and PM 2.5 , respectively.The dust storms were observed for 65 no. of hours during the study period out of which only 56 no. of hours, the monitoring were conducted.Therefore, the percentage of monitoring hours carried out during rain and dust storms for NO 2 and PM 2.5 are 3.8% and 3.2% respectively.The percentage of monitoring hours during rain and dust storm period are very less and does not impact the distribution patterns of pollutant concentration if removed from the data set.
The monitoring station is located at 28°37'40.83"Nand 77°4'28.14"E at an altitude of 221 m above msl and at 12 meters distance from the BSZ road in west direction.The NO 2 and PM 2.5 concentrations were monitored by advanced instrumentations i.e., gas analyzer model number AC 31 (chemiluminescence based) and beta gauge based particulate matter analyzer, MP101 (Environnment S.A., 2016) as per CPCB norms (CPCB, 2011).The CPCB ensures minimum uncertainty in ambient air quality monitoring by defining stringent protocols (CPCB, 2011) for the sampling/analysis/ calibration methods and implementation of Quality Assurance /Quality Control programs (QA/QC).
At APH-2, one hour average ambient PM 2.5 concentrations data for winter (January-February, 2009) and summer (March-May, 2009) seasons were collected from IIT Madras air quality laboratory.The PM 2.5 concentrations were monitored using portable environmental dust monitor (GRIMM-107, Make GRIMM Aerosol Technik, Gmbh & CO.) at kerbside (IIT Madras gate) of SP Road.The instrument kept at kerbside of SP road (13°00'23.48"Nand 80°14'28.79"E)at an altitude of 12 m above msl.The instrument is located at a distance of 10 m in the south of SP road.The ambient NO 2 concentrations data were not measured at APH-2.Further, the missing hour values were not considered in the distribution plot.No dust storm and rain were observed during the monitoring period at APH-2.

Status of PM 2.5 and NO 2 Level
This section describes the status and spread in PM 2.5 and NO 2 concentrations at selected urban hotspots in Delhi and Chennai cities.The mean of hourly NO 2 concentrations in winter and summer periods were found to be 84.01 ± 73.99 µg m -3 and 70.84 ± 62.70 µg m -3 , respectively, which indicate high pollution burden during winter season due to the prevalence of inversion conditions (Table 2).The skewness was 1.95 and 2.37 in winter and summer, respectively.Similarly the kurtosis value for these periods were found to be 4.14 and 7.54, respectively which indicate that data skewed more toward right side of mean.Similarly, the mean of hourly PM 2.5 concentrations in winter and summer were found to be 173.03± 79.20 µg m -3 and 129.29 ± 77.19 µg m -3 , respectively.The skewness and kurtosis were found to be 0.56, 1.50 and 0.77, 2.50, respectively for winter and summer seasons, indicated longer tails than the normal distribution.
Like APH-1, the mean of hourly PM 2.5 concentrations were found to be high during winter (66.90 ± 31.98 µg m -3 ) season when compared to summer (39.28 ± 20.94 µg m -3 ) at APH-2.This was due to poor dispersion condition in winter season.Further, skewness and kurtosis values clearly described that the distribution form have longer tails than those in the normal distribution (Table 3).

Exceedances of PM 2.5 and NO 2
This section describes the execcedances of PM 2.5 and NO 2 concentrations over the specified air quality standards and their correlation with wind speed and direction.It was expected that the probability of occurrence of extreme pollutant event would be more during winter due to the low assimilative capacity of the atmosphere compared to summer season.The hourly average NO 2 and PM 2.5 concentrations were compared with WHO guidelines i.e., hourly average PM 2.5 = 200 µg m -3 (WHO, 2005) and NO 2 = 80 µg m -3 (Fu et al., 2000;DEQ Idaho, 2001).
Fig. 2 describes the frequency of exceedences of NO 2 concentrations over 200 µg m -3 during winter and summer at APH-1.Hourly average NO 2 concentrations were found to be 7.5% of times exceeding the specified guidelines, out of which 7.2% were in the range of 201-400 µg m -3 and 0.3% in the range of 401-500 µg m -3 .It was also observed that the maximum frequency of exceedences occurred when wind speed were found to be ≤ 0.5 m s -1 (calm) followed by the wind speed range of 0.6-2.0m s -1 blowing from northeast and east-northeast.During summer, NO 2 concentrations were found to be 5.6% of time exceeding 200 µg m -3 , out of which 5.3% of time were in the range of 201-400 µg m -3 and 0.3% in the range of 401-500 µg m -3 .The frequency of exceedances was found to be more when wind speed were ≤ 0.5 m s -1 irrespective of the wind direction and with wind speed range of 0.6-2.0m s -1 (Fig. 2(b)).On the other hand, at APH-2, hourly PM 2.5 was found to be 92% of the times exceeding the specified standard during winter (Fig. 3(a)).Out of which 43% of times were in the range of 81-160 µg m -3 , 26% of times were in the range of 161-240 µg m -3 and 23% of times were in the range 241-540 µg m -3 .However, during summer, 72% were found to be exceeded the standards.Out which 46% of the times were in the range of 81-160 µg m -3 , 16% of the time were in the range of 161-240 µg m -3 and 10% of the time were in the range of 241-540 µg m -3 (Fig. 3(b)).
Highest pollutant concentrations (Fig. 1) were observed when wind were blowing from northeast, east and southeast directions and with a wind speed of ≤ 0.5 m s -1 (calm wind).No major polluting industries are located near monitoring station in the southeast directions because no industry are allowed to operate in Delhi city (Bentinck and Chikara, 2000).As expected, the pollutant concentration were exceeded the air quality standards more during winter compared to summer season.
At APH-2, PM 2.5 concentrations were found to be 25% of the time exceeded the standard i.e., 80 µg m -3 .Out of which 23% of times were in the range of 80-160 µg m -3 and 2% were in the range of 161-240 µg m -3 .However, in summer, it was 5% exceeded the specified standard which was in the range of 80-160 µg m -3 (Fig. 4).Therefore, PM 2.5 values were found exceeding the standard when the wind occurs from east and with low speed (calm).The percentage of exceeding was more in winter season when compared to summer season.The differences in PM 2.5 and NO 2 concentrations exceedance as observed between APH-1 and APH-2 are due to differences in emission strength of the sources and meteorology.The difference in meteorological conditions between APH-1 and APH-2 along with windrose diagram is discussed in supplementary information (SI) section S1.In addition to these parameters, the occurrence of rain, variation in temperatures and relative humidity and solar radiation can significantly influence the distribution patterns of any air pollutant.The difference in emission rate of pollutant from source and geography of the study site may also impact the distribution patterns.Gokhale and Khare (2007);McConnell et al. (2010); Gulia et al. (2015) and Sunil (2015) have described the implications of such exceedances in PM 2.5 and NO 2 concentrations over specified standards in ambient environment through analyzing various

The Study Location APH-1
This section explains the distribution pattern of PM 2.5 and NO 2 concentrations, which are highly influenced by pollutant emission from source, meteorological conditions and site features.The values of KS (0.03), AD (1.98) and Chi-square (54.99) were found to be the lowest for the lognormal distribution model with a significance level of 0.05 compared to test statistics of other selected distribution model during winter (Table 4).However, in summer, these values were 0.04, 3.13 and 63.48, respectively and found to be the lowest for log-logistic distribution model.Hence, NO 2 concentrations data followed lognormal and loglogistic distribution in winter and summer, respectively, at APH-1 (Fig. 5).In one of the studies, Sharma et al. (2013b) have also observed that 24 hour average NO 2 concentration data of year 2003 to 2006 that include all seasons follows log-logistic distribution at one of the urban locations in Delhi city.The probability plot of NO 2 for winter and summer seasons also indicates satisfactory fitting throughout the distribution with confidence interval of 95 percent (Fig. 5).
For PM 2.5 , the KS, AD and Chi-square test values of 0.08, 2.29 and 39.22, respectively, were found to be the lowest for lognormal distribution with a significance level of 0.05 compared with test statistics values of other selected distribution models (Table 5).Similarly, in summer, these values were 0.05, 5.29 and 82.83, respectively and found to be the lowest for lognormal distribution.Therefore, it is inferred that PM 2.5 concentration data follow lognormal distribution in both winter and summer seasons at APH-1.In the past, the studies (Kan and Chen, 2004;Giavis et al., 2009;Papanastasiou and Melas, 2010;Sharma et al., 2013b) were reported that daily average of ambient PM concentrations best fit the lognormal distribution.The probability plot of lognormal distribution of PM 2.5 also indicates satisfactory fitting throughout the distribution with confidence interval of 95 percent (Fig. 6).

The Study Location APH-2
The KS, AD and Chi-square values of 0.03, 1.89 and 39.70, respectively, were found to be the lowest for lognormal distribution with significance level of 0.05 compared with test statistics of other selected SDMs in winter.Similarly, in summer, these values were 0.039, 1.42 and 28.91, respectively and found to be the lowest for lognormal distribution.Hence, lognormal distribution was fitted to be the best to hourly PM 2.5 concentrations in winter as well as summer seasons (Table 6).The probability plot of lognormal distribution of PM 2.5 also indicates satisfactory fitting throughout the distribution with confidence interval of 95 percent (Fig. 7).
It is observed that PM 2.5 concentration distributions at     At APH-1, the exceedences of hourly average NO 2 concentrations were predicted to be 9% and 6.4% during winter and summer seasons, respectively.Similarly, exceedences of hourly average PM 2.5 concentrations over specified standard were predicted to be 93.1% and 72.8%, respectively.On the other hand, the exceedences of hourly average PM 2.5 concentration over standard were predicted to be 26.98% and 5.48% during winter and summer seasons, respectively.The exceedances of predicted and monitored pollutant concentration were observed to be in agreement (Section 4.2).

CONCLUSIONS
This study evaluated the distribution patterns of PM 2.5 and NO 2 and their frequency of exceedances over specified standards/guidelines at two urban air pollution hotspots in Delhi and Chennai cities.The hourly concentration data for PM 2.5 and NO 2 were analysed with the aim to quantify the seasonal variability of their concentrations, their correlations with meteorological parameters and their best fit statistical distribution model.
The following conclusions were drawn: • High variability in both NO 2 and PM 2.5 concentrations were found in winter and summer seasons at APH-1.At APH-2, the hourly PM 2.5 concentrations were found to be high during winter (66.90 ± 31.98 µg m -3 ) compared to summer (39.28 ± 20.94 µg m -3 ) at APH-2.• Hourly average NO 2 and PM 2.5 concentrations were exceeded upto 3 and 5 times, respectively over the specified NAAQS standards/WHO guidelines in both winter and summer seasons at AHP-1.However, at AHP-2, PM 2.5 was exceeded by 8% and 4% of the times during winter and summer seasons, respectively.• At APH-1, the NO 2 concentrations were fitted with lognormal and log-logistic model for winter and summer seasons, respectively.It implies that the distribution pattern of NO 2 show significant influence of meteorology and their reactive nature in two different climatic conditions.On the contrary, PM 2.5 concentrations of both winter and summer seasons at APH-1 and APH-2 were fitted with the lognormal model.This might be due to its less reactivity and particle nature compared to NO 2 , which is gaseous.• The frequency of exceedances of predicted and monitored concentrations of NO 2 and PM 2.5 were found in agreement.Therefore, statistical distribution model are efficient to satisfactorily predict the extreme range of air pollutants concentration.

Fig. 1 .
Fig. 1.Selected air pollution hotspots in Delhi and Chennai cities.

Fig. 2 .
Fig. 2. Exceedance of hourly NO 2 concentrations over WHO guidelines during winter (a) and summer (b) at APH-1.

Fig. 3 .
Fig. 3. Exceedance of hourly PM 2.5 concentrations over air quality standards during winter (a) and summer (b) at APH-1.

Fig. 4 .
Fig. 4. Exceedance of hourly PM 2.5 concentrations over air quality standards during winter (a) and summer (b) at APH-2.

Fig. 9 .F̅
Fig. 9. Curve fitting of best fit distribution model on histogram by using estimated parameters at APH-2.

Table 1 .
Some of the past studies describing fitting of statistical distribution model for air pollutant.

Table 2 .
Summary of basic statistics of NO 2 and PM 2.5 concentrations at APH-1.

Table 3 .
Summary of basic statistics of PM 2.5 concentration at APH-2.

Table 4 .
Goodness of fit test statistics for NO 2 concentrations at APH-1.

Table 5 .
Statistical distribution models for PM 2.5 concentrations at APH-1.

Table 6 .
Statistical distribution models for PM 2.5 concentrations at APH-2.