The Impact of Air Pollutants and Meteorological Variableson Visibility in Delhi

P. Goyal & Anikender Kumar & Dhirendra Mishra

Received: 14 March 2011 /Accepted: 21 August 2013 /Published online: 6 September 2013# Springer Science+Business Media Dordrecht 2013

Abstract A study has been made to analyze the impact of airpollutants and meteorological variables on visibility in Delhi,for the years 2003–2006. The correlation matrix of dailyvisibility, meteorological variables, and air pollutants concen-tration during the period has been studied. The matrix reflectsthe negative values of the correlation coefficient of visibilitywith respirable suspended particulate matter, suspended par-ticulate matter, relative humidity, and, positive values with drybulb temperature, maximum temperature, minimum tempera-ture, and sunshine hours. The annual average visibility hasbeen estimated as approximately 2.77 km. Furthermore, it isfound to be maximum in monsoon, followed by summer,post-monsoon, and winter seasons. It is also noticeable thatthe visibility is always higher in rainy days when comparedwith that in dry days. Similarly, the annual average visibilityduring the weekends is found to be higher than that in theweekdays. The daily visibility has been forecasted throughtwo statistical techniques namely, multiple linear regression(MLR) and principal component regression (PCR). The re-sults obtained from these two techniques have been evaluatedby comparing with observed data. This proves satisfactoryperformance of both the techniques. In addition, it reflects thatthe PCR performs better than the MLR technique.

Keywords Air pollutants . Meteorological variables .

Visibility . Principal component regression

1 Introduction

Manmade pollutants from combustion, construction, mining,agriculture, welfare, etc. are increasing significantly in the air.

It is well known that atmospheric visibility (VV) can bereduced by the absorption and scattering of light by aerosols(particulates) in the atmosphere. The aerosols start to changetheir equilibrium sizes, when relative humidity (RH) tends tobe 100 %, and, consequently, have effect on light scattering[1]. The variation in RH is seen to account for most of thechanges in VV. The other meteorological variables can alsoaffect the VV as the scattering coefficient is affected by drybulb temperature (DBT) during the day [2, 3]. The DBT is thetemperature of air measured by a thermometer freely exposedto the air but shielded from radiation and moisture [4].Wind isthe natural horizontal motion of the air in the atmosphere. At alocal area, wind patterns affect the pollutant concentration.High wind speeds decrease the concentration of pollutants;wind dilutes and disperses the pollutants, which in turn affectsthe atmospheric VV.

The effect of air pollutants on VV was shown first timeduring the London smog of 1952, in which the VV wasreduced to near zero by Brimblecombe [5]. An atmosphericVV trend was also discussed in an urban area of Taiwan byTsai [6]. Generally, most of the studies related to VV wereconducted in developed countries; very few studies have beenconducted in developing countries. India, the largest develop-ing country in the world, has undergone a rapid developmentin the last two decades. Consequently, the air pollution inIndia has been recorded as one of the highest in the world.The city of Delhi, the capital of India, is one of the ten mostpolluted cities in the world, as pointed out by theWorld HealthOrganization. The main causes are the high growth in popu-lation rate and the economic activity, which are resulting inincrease of transport. The number of vehicles in Delhi isaround 5.6 million, as per Economic Survey of Delhi [7].The respirable suspended particulate matter (RSPM) of size≤10 μm in diameter and suspended particulate matter (SPM)of size ≤100 μm in diameter are found to be the majorpollutants in Delhi, which exceed the prescribed limits ofNational Ambient Air Quality Standards (NAAQS). Theseare emitted from vehicles, industries, and power plants.

P. Goyal (*) :A. Kumar :D. MishraCentre for Atmospheric Sciences, Indian Institute of TechnologyDelhi, Hauz Khas, New Delhi 110016, Indiae-mail: pramila@cas.iitd.ernet.in

Environ Model Assess (2014) 19:127–138DOI 10.1007/s10666-013-9380-4

The previous studies, based on the historical data of airpollutants and their impact on local VV, reveal that the atmo-spheric VV has been gradually deteriorating in Delhi in the lastthree decades. Thus, there is a need of monitoring, modeling,and forecasting of the criteria pollutants in the air. The regula-tory agencies are monitoring daily air quality at different loca-tions all over Delhi. The several deterministic models are foundto be available to evaluate and predict the pollutant dispersionin urban areas. However, the Gaussian dispersion models havebeen generally used in most of the air pollution modellingstudies for predicting the concentration of air pollutants. Inrecent years, a large set of comprehensive and reliable 3DEulerian chemistry-transport models, such as CommunityMultiscale Air Quality [8] and Polair3D [9] have also beenused for air quality studies for regulatory purpose in manycountries. Although dispersion models have some physicalbasis, detailed information about the sources of pollutants andother parameters are always not known [10]. An alternative tothe dispersion models, to overcome their limitations, is theapplication of statistical models, which can be used to facilitatethe prediction of pollutant concentrations [11, 12]. Many stud-ies using the statistical models have been conducted to forecastconcentration of pollutants based on the local meteorologicalconditions [13]. Shi and Harrison [14] developed a regressionmodel for the prediction of NOx and NO2 in London. Thenonlinear models like Neural Network have also been used toforecast the pollutant concentrations [15]. One of the importantadvantages to use the regression-based models is that they donot need expensive computational resources. A regressionmodel was also used by Cogliani [16] for air pollution forecastin Florence, Milan, and Vicence cities. The source apportion-ment of VV degradation is also investigated using the multiplelinear regression (MLR) techniques [17]. Recently, Kumar andGoyal [18] applied the principal component analysis (PCA)with MLR to improve the forecasting of AQI in Delhi. Themost of the earlier studies of VV have beenmade in foggy days,which are considered the main cause of disturbance in takeoffand landing of the aircrafts. The above discussion reflects thatvery few studies of forecasting of VVhave beenmade for urbancities of India. Therefore, the main objective of the presentstudy is to forecast the daily VV and assess the impact of airquality and meteorological variables on VV in Delhi.

2 Description of the Case Study and Data

Delhi is situated in the northern part of India (Latitude 28°35′N, Longitude 71°12′ E). The river Yamuna forms the Easternboundary of the city. Delhi is situated between the GreatIndian Desert (Thar Desert) of Rajasthan state in the West,the Central hot plains to the South, and the cooler hilly regionof the North and East. The pre-monsoon (March to May) isgoverned by high temperature and high winds, while the

monsoon (June to September) is dominated by rains andpost-monsoon (October and November) has moderate temper-ature and wind conditions. The average annual rainfall inDelhi is 714 mm, three fourths of which fall in July toSeptember [7]. Given the worst meteorological scenario, themost important season in Delhi is the winter, lasting fromDecember to February. The cold waves from the Himalayanregion make the winter very chilly. Temperatures fall substan-tially down to as low as 3 to 4 °C at the peak of winter.However, the winds are generally light to moderate. Theaverage annual daily minimum (MinT ) and maximum tem-peratures (MaxT ) are 18.9 and 31.2 °C, respectively. Thehottest month is May having daily MaxT and MinT as 39.5and 25.9 °C, respectively. The coolest month is January hav-ing daily mean MaxT and MinT as 20.8 and 7.6 °C, respec-tively. Fog is a persistent winter phenomenon in Delhi and canbe described as the regular feature during the winter months.The weather condition that prevails over the city during thewinter months permits the quick fog in the early morning andevening. The problem of fog in Delhi is faced almost everyyear. The winter fog of Delhi often thickens to such an extentthat the normal life of the city is brought to a standstill.

The ambient air quality of air pollutants has been moni-tored at different stations, which have been categorized on aland use basis by Central Pollution Control Board (CPCB)[19] like industrial and residential. The stations in the residen-tial areas are Sarojini Nagar, Town Hall, Nizamuddin, AshokVihar, Sirifort, and Jankpuri and in Industrial areas areMayapuri, Shahzada Bagh, and Shahdara. The results of mon-itored ambient air quality parameters for the period 2004–2006 show that the annual average concentration of RSPMvaries between 140 and 216 μg/m3 at industrial locations and99 to 161 μg/m3 at residential locations. Similarly, the SPMvaries 350 to 497 μg/m3 at industrial locations and 321 to496 μg/m3 at residential locations.

Air quality data of RSPM and SPM for the years 2003 to2006 at Income Tax Office (ITO) has been used in the presentstudy, which is one of busiest traffic intersections in center ofthe city and is a continuous air quality monitoring station ofCPCB. Therefore, the study at ITO junction is very importantfrom the point of view of traffic. The daily meteorologicalparameters, namely, VV, DBT, RH, rainfall (RF), wind speed(WSp), wind direction index (WDI), radiation (RD), vaporpressure (Vp), MaxT, MinT, sunshine hour (SSH), stationlevel pressure (SLP), and cloud cover (CC) for the years 2003–2006, monitored by the Indian Meteorological Department atthe Safdarjung Airport (Fig. 1), have been used. It is notice-able that wind direction index (WDI) is used in place of winddirection (WD), to avoid the discontinuity. WDI is definedaccording to the following equation [20].

WDI ¼ 1þ Sin ϕ−π=4ð Þ; ð1Þwhere ϕ is the WD in radians.

128 P. Goyal et al.

The two statistical models, namely, MLR and PCR are usedfor forecasting the daily VV. The formulations of these modelsare explained in Appendix A.

3 Results and Discussion

3.1 Variation of VV

The seasonal variation of VV during four consecutiveyears 2003–2006 has been studied and shown graphically inFig. 2. The variation pattern is observed to be almost the samein all the four seasons. The annual average VV has beenestimated as 2.77 km approximately and is found to be max-imum in monsoon followed by summer, post-monsoon, andwinter seasons. The standard deviation is also found to be themaximum as 3.54 km in monsoon, followed by 2.89, 2.51,and 1.80 km respectively during summer, post-monsoon, andwinter seasons. Similarly, the monthly variation of VV, yearwise, has been shown in Fig. 3, which indicates that theminimum values are observed during December and January(winter season) and maximum during April andMay (summerseason). However, the overall yearly variation of VV is found

to be maximum in May 2004 and minimum in January 2003.The standard deviations of yearly VVare 0.54, 0.55, 0.58, and0.71 km for the years 2003, 2005, 2006, and 2004, respec-tively. It is also well understood that the rain/precipitation alsoaffects VV, as shown in Table 1. However, the yearly percent-age of rainy days varies from 14.24 to 47.94, with an averagevalue of 27.50. The VV in rainy day means the VV measuredduring the entire rainy day. The standard deviations of VVarealso found as 0.93 km and 1.04 km for rainy and non-rainydays, respectively. It is also clear from Table 1 that the VV ishigher in rainy days compared with dry/non-rainy days, whichmay be due to the washing out of pollutants by rain, resultinginto reduction in the concentration of pollutants, or, in otherwords, increase in VV. On the basis of above results anddiscussions, it is concluded that the VV has not been goodin Delhi, which is also consistent with the studies by Singhet al. [21], Schichtel et al. [22], and Husar et al. [23].

3.2 Relationships Among VV, Meteorological Variables,and Concentration of Pollutants

The scatter plot matrix and correlation of daily VV, meteoro-logical variables and concentration of air pollutants have been

N

ITO (Air quality monitoring station)

Safdarjung (Meteorological Station)

ITO

Safdarjung Airport

Fig. 1 Map of Delhi with air quality monitoring station (ITO) and meteorological station (Safdarjung airport)

Impact of Air Pollutants and Meteorological Variables 129

studied and analyzed as shown in Fig. 4 and Table 2, respec-tively. Figure 4 represents the pair-wise scatter plot betweenthe variables, where each row and column defines a singlescatter plot. This matrix provides the relationships between thevariables and the nature of these relationships.

Table 2 reflects that the correlations between most of thevariables are not poor as their values are more than 0.0677,which represents that correlation coefficient is significant.Since the critical value of correlation coefficient at the 99-percentile confidence interval using Student's t test for thestudy period is found to be 0.0677, which is statisticallysignificant. It has been found that VV has negative correlation(inversely proportional) with RSPM, SPM, SLP, and RH. Theatmospheric RH tends to be >80 %, RSPM and SPM absorb

moisture and are growing rapidly in size, i.e., the resultantincreased scattering may lead the reduction in VV [2, 3]. Thedecrease in SLP enhances low pressure as well as precipitation,which may reduce the concentration of pollutants, i.e., in-creased VV. The VV has better correlation with Vp comparedwith many other meteorological variables since while Vpincreases beyond the saturation point, there is reduction inthe capability of atmosphere to restore the pollutants, whichleads to low concentration of pollutants, i.e., increased VV.

It has also been found that VV has positive correlation(directly proportional) with many variables such as MinT,DBT, Vp, MaxT, SSH, CC, WSp, RD, and RF. The concen-tration of pollutants can be reduced by increasing surface DBT,MaxT, and MinT, which lead to high VV. The reduction in

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solar RD results into low temperature and low boundary layerheight, which lead to high concentration of pollutants, i.e., lowVV. It is a well-known fact that the high wind speed causes lowconcentration of pollutants, i.e., high VV. The average concen-tration level of RSPM and SPM are found to be increased from156 to 238 μg/m3 and from 361 to 524 μg/m3, in rainy andnon-rainy days, respectively. However, the average VV de-creases from 3.21 km in rainy days to 2.61 km in non-rainydays, which shows that there is direct relationship between VVand precipitation. VV is directly proportional to SSH, which isrelated to solar RD. The CC and VV are also directly

proportional to each other, which is also supported by the factthat the presence of CC reduces the concentration of RSPMand SPM.

3.3 Analysis of VVand Air Pollutants in Weekdaysand Weekends

Delhi, one of the most populous cities in India, has trans-portation as one of the major sources of air pollutants. Ithas a total vehicular population of about 6 million, which ismore than the combined vehicular population of Mumbai,Kolkata, and Chennai [24, 25]. This vehicular populationand the consequent higher traffic volume on the city roadshave put the transportation system in the city under heavystress, with the situation getting worse gradually. Generally,the number of private vehicles in Delhi is very large. Theweekly cycle of high density of traffic in Delhi is alsodiscussed by Gokhale and Pandian [26]. It is observed inDelhi that the traffic is higher during weekdays whencompared with that in weekends. Thus, the number ofprivate vehicles plying on the roads on weekdays is higherin comparison to that during weekends, which results intoincreased pollutants on weekdays. The observed concentra-tions of RSPM and SPM are found to be 241 and 527 μg/m3

Table 1 Visibility observations of rainy and non-rainy days, 2003–2006

Year Totalobservation

Rainyvisibility

Non-rainyvisibility

% of observations

Days km Days km Made in rain

2003 365 80 2.94 285 2.40 21.91

2004 366 96 3.19 270 2.69 26.22

2005 365 175 3.27 190 2.61 47.94

2006 365 52 3.42 313 2.71 14.24

Fig. 4 Scatter plot matrix ofinput variables for theyears 2003–2006

Impact of Air Pollutants and Meteorological Variables 131

on weekdays, as compared with 236 and 518 μg/m3 onweekends, during the study period. The high concentrationsof RSPM and SPM during weekdays cause more scattering ofsunlight when compared with that in the weekends. This hasbeen termed as the weekend effect. The standard deviations ofRSPM and SPM are 120.04 and 224.64 and 121.44 and237.82 μg/m3 during weekends and weekdays, respectively.The average annual VV is found to be 2.79 km, duringweekends, slightly higher than 2.74 km on weekdays, which

shows a difference of 0.05 km only. This is insignificant and,therefore, it is considered negligible for model predictions/forecasting. The graphical presentation of the VV in rainy andnon-rainy days during the weekdays and weekends is shownin Fig. 5, which shows that the mean and standard deviation ofVV during rainy weekend and rainy weekday are 3.22 and0.93 and 3.19 and 0.93 km, respectively. The same for non-rainy weekends and non-rainy weekdays are found to be 2.61and 1.04 and 2.59 and 1.03 km respectively, which reveal that

Table 2 Correlation matrix of daily visibility, meteorological parameters, and air pollutants in Delhi 2003–2006

VV RSPM SPM DBT RH Vp RF WSp WDI RD MaxT MinT SSH SLP CC

VV 1.00

RSPM −0.39 1.00

SPM −0.39 0.74 1.00

DBT 0.60 −0.08 0.01 1.00

RH −0.15 −0.32 −0.37 −0.44 1.00

Vp 0.59 −0.29 −0.29 0.70 0.17 1.00

RF 0.07 −0.11 −0.12 0.07 0.14 0.18 1.00

WSp 0.19 0.04 −0.05 0.07 −0.28 0.00 0.01 1.00

WDI −0.04 0.00 −0.01 −0.06 −0.04 −0.04 0.05 0.21 1.00

RD 0.24 0.04 0.07 0.43 −0.43 0.10 −0.02 0.05 −0.01 1.00

MaxT 0.52 0.02 0.11 0.96 −0.56 0.57 0.06 0.03 −0.05 0.46 1.00

MinT 0.63 −0.16 −0.08 0.97 −0.27 0.79 0.10 0.08 −0.08 0.34 0.88 1.00

SSH 0.29 −0.06 −0.09 0.24 −0.52 −0.08 −0.07 0.18 −0.01 0.39 0.32 0.12 1.00

SLP −0.57 0.16 0.06 −0.88 0.22 −0.78 −0.13 −0.07 0.06 −0.31 −0.80 −0.90 −0.05 1.00

CC 0.29 −0.23 −0.19 0.30 0.23 0.50 0.14 −0.11 −0.12 −0.02 0.18 0.39 −0.15 −0.43 1.00

VV visibility, RSPM respirable suspended particulate matter, SPM suspended particulate matter, DBT dry bulb temperature, RH relative humidity, Vpvapor pressure, RF total rainfall,WSp wind speed,WDI wind direction index, RD radiation,MaxT maximum temperature,MinT minimum temperature,SSH sunshine hours, SLP station-level pressure, CC cloud cover

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Fig. 5 The variation of visibilityin rainy weekend, non-rainyweekend, rainy weekday, andnon-rainy weekday during2003–2006

132 P. Goyal et al.

maximum and minimum VVare observed during rainy week-ends and non-rainy weekdays, respectively.

3.4 Evaluation of the Model's Performance

The forecasting of daily VV, based on air pollutant con-centration and meteorological variables, has been madeusing MLR and PCR techniques during winter season forthe years 2003–2005. The models' daily air quality fore-casting for the year 2006 has been validated with observeddata for the same year. To avoid the asymptotic effect, theinput and output data are normalized between −1 and +1before preprocessing using the minimum and maximum ofthe time series data. The methodology of both the tech-niques is described in Appendix A.

Firstly, the equation based on MLR technique has beendeveloped on the basis of daily data of winter season duringthe years 2003–2005, as given below:

VV½ � ¼ − 0:09 þ 0:47 PDVV½ � − 0:01 RSPM½ � − 0:15 SPM½ � − 0:19 DBT½ � − 0:20 RH½ � − 0:02 Vp½ �þ0:01 RF½ � þ 0:07 wsp½ � þ 0:01 WDI½ �−0:04 RD½ � þ 0:05 MaxT½ � þ 0:26 MinT½ � þ 0:12 SSH½ �−0:02 SLP½ � þ 0:05 CC½ �

ð2Þ

The above equation (2) is used to forecast daily VV inthe year 2006, which has been compared with observeddaily VV of 2006, which has been analyzed throughstatistical error analysis as shown in Table 3. This indi-cates that model is performing satisfactory with respect tothe normalized mean square error and root mean squareerror. However, the model is overpredicting with respect tofractional bias. The coefficient of correlation (R) has been

found at 0.78, which is significant as the critical value forcorrelation coefficient at 99-percentile coefficient intervalusing Student's t test is 0.1602 and also according toChung's scale [27]. The model's training for theyears 2003–2005 and validation in 2006 between observedand forecasted values have been shown graphically inFig. 6a, b, respectively. The above discussion reflects thesatisfactory performance of the MLR model.

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Fig. 6 Scatter plots between daily observed and MLR model forecasted visibility in a training and b validation period

Table 3 Statistical error analysis between observed and MLR modelpredicted visibility in training and validation periods

Statistical error Training period(2003–2005)

Validation period (2006)

RMSE 540.68 820.37

NMSE 0.0865 0.1861

Correlation coefficient 0.7837 0.5223

FB −4.4678E−07 −0.2358

FAC2 (%) 94.83 88.89

NMSE normalized mean square error, RMSE root mean square error

Impact of Air Pollutants and Meteorological Variables 133

The other model is the PCR model, whose equation hasbeen developed for the same data of the years 2003–2006.However, the data of the years 2003–2005 has been used todetermine the covariance matrix. The predictor variables ofthe regression equation are transformed into principal com-ponents (PCs) through an eigenvalue matrix of variables,which explain most of the total variation in the data. The

eigenvalue and amounts of variance, explained by PCs,whose cumulative variance is approximately 85 %, areconsidered for further calculation (Table 4). The rest ofthe components are ignored. Therefore, now only 8 newvariables (PCs) are used instead of original 15 variables.The loadings (or coefficients) of each input variable corre-sponding to all eight PCs are made.

Table 4 Factor loadings for visi-bility, air pollutants, and meteo-rological variables in Delhi duringwinter season of the period of2003–2005

Component PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8

Eigenvalue 4.43 2.07 1.92 1.21 1.09 0.90 0.82 0.64

Cumulative eigenvalue 4.43 6.49 8.41 9.62 10.71 11.61 12.43 13.08

% total variance 29.52 13.77 12.77 8.09 7.27 6.00 5.46 4.30

Cumulative variance % 29.52 43.29 56.06 64.16 71.42 77.42 82.88 87.17

Variables

PDVV −0.29 0.19 0.08 0.00 −0.17 −0.19 0.23 −0.15

RSPM −0.18 −0.26 0.09 −0.03 0.50 0.07 0.26 0.09

SPM −0.18 −0.20 0.01 0.00 0.62 0.05 0.08 0.03

DBT −0.14 0.31 −0.03 0.34 0.07 0.14 0.06 0.04

RH 0.14 −0.27 −0.09 0.17 −0.17 0.05 −0.13 −0.24

Vp −0.22 0.04 −0.10 0.33 0.04 −0.08 −0.49 −0.22

RF −0.60 −0.17 −0.05 −0.01 −0.01 −0.20 −0.30 −0.37

WSp −0.43 0.04 −0.16 −0.28 −0.21 −0.36 0.38 0.17

WDI 0.06 0.16 −0.92 −0.23 0.13 0.14 −0.04 −0.03

RD 0.10 0.26 0.12 −0.19 0.11 0.22 0.34 −0.79

MaxT −0.08 0.32 0.01 0.25 0.29 0.12 −0.09 0.07

MinT −0.08 0.25 −0.06 0.48 −0.19 0.11 0.27 0.07

SSH −0.15 0.54 0.26 −0.47 0.07 0.16 −0.39 0.19

SLP 0.17 −0.19 0.08 −0.24 −0.09 −0.03 −0.17 −0.12

CC −0.38 −0.27 0.01 −0.09 −0.31 0.80 0.03 0.09

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134 P. Goyal et al.

The PCR model for winter season, based on the transferreddata of the years 2003–2005, has been developed and analyzed

statistically as discussed in Appendix A. The forecasting equa-tion of the PCR model for the winter season is shown below:

VV½ � ¼ −0:0091−0:2820x PC1½ � þ 0:2206 PC2½ � þ 0:0568x PC3½ �−0:0688x PC4½ �−0:1956x PC5½ �0:1208 x PC6½ � þ 0:1227 x PC7½ � þ 0:0189 x PC8½ � ð3Þ

The first PC (PC1), out of eight PCs, associated with thegreatest eigenvalue and total variance of 29.52 %, repre-sents the linear combination of the variables, which ac-counts for the maximum total variability in the data. Thesecond and third PCs (PC2 and PC3) as 13.77 and 12.77respectively, explain the maximum variability. However,they are not accounted by the PC1. The above equation(3) is used to forecast daily VV through training of airquality and meteorological data of the years 2003–2005and validation for the year 2006, which have been com-pared with observed data of the corresponding years and arerepresented in Fig. 7a, b. The forecasted annual averageVV, using MLR and PCR models for winter season of

years 2003–2006, has been compared with observed VVin Fig. 8, which shows that PCR model is performing betterthan MLR model. The statistical evaluation between ob-served and model's forecasted values for 2003–2005 and2006 has also been made for PCR in Table 5, which showsthat PCR model is performing satisfactory and found betterthan the MLR model. The advantage of the PCR techniqueover MLR lies in its characteristics, handling large andhighly interrelated (multicollinearity) sets of data. The re-lationship between observed concentration of pollutants ormeteorological variables and VV is expected to be non-linear.However, the same relationship, obtained from both themodels (PCR and MLR) is linear. Thus, the model resultsare considered to be biased with respect to observation.

The above results and discussions reveal that VV has beengradually reducing during the study period, which may be dueto increased concentration of air pollutants specially RSPMand SPM. Their concentrations have always been found to beexceeding the prescribed NAAQS in Delhi.

4 Conclusions

It is observed from the historical data and modeling studiesthat the atmospheric VV has been gradually deteriorating in

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Fig. 8 Comparison of annualforecasted visibility using MLRand PCR models for winterseason of years 2003–2006

Table 5 Statistical error analysis between observed and PCR modelpredicted visibility in training and validation period

Statistical error Training period(2003–2005)

Validationperiod (2006)

RMSE 494.69 573.03

NMSE 0.0724 0.1047

Correlation coefficient 0.8228 0.5512

FB −4.679E−07 −0.0942

FAC2 (%) 96.31 90

Impact of Air Pollutants and Meteorological Variables 135

Delhi over last three decades. However, no extensive study ofeffect of major air pollutants and meteorological variables onVV has been made for Delhi. Therefore, in the present study,the same has been attempted for air quality andmeteorologicaldata for the years 2003–2006. The annual average VV hasbeen estimated as 2.77 km approximately and is found to bemaximum in monsoon followed by summer, post-monsoon,and winter seasons. The VV is also found to be higher in rainydays when compared with that during the non-rainy days. It isalso noted that annual average VV during weekends is2.79 km, which is slightly higher than 2.74 km in weekdays.The correlation matrix of daily VV, meteorological variables,and air pollutant concentration during the study period indi-cates that the VV has negative correlation with RSPM, SPM,SLP, and RH, and positive correlation with MinT, DBT, Vp,MaxT, SSH, CC, WSp, RD, and RF. The daily VV has beenforecasted through MLR and PCR models using daily timeseries data of the years 2003–2006. However, both the modelsare found to be performing satisfactorily and the results ofPCR are found to be better than MLR. The number of predic-tors and complexity are also reduced in PCRmodel. The samemodel can also be used for other urban cities of India toforecast the VV.

In conclusion, the above study is considered useful for dailyforecasting of VV, which would be helpful to the concernedauthorities for providing necessary information to the generalpublic. However, the above models are time series model anddo not contain the information of sources of air pollutants anddispersion parameters. Therefore, it would be better to use theintegrated model, coupling of statistical models and air disper-sion models, for forecasting the VV. As the present models arelinear models with certain limitations, nonlinear model asneural network would be a better choice. The study wouldhave been more generalized if it had been conducted at differ-ent locations in Delhi. However, because of non-availability ofcontinuous monitoring air quality data at different locations, ithas been made only at one location. The accuracy of VV maybe increased by using the air quality and meteorological data,observed simultaneously at the same place.

Appendix A

Daily VV Forecasting Model Development

A forecast can be expressed as a function of a certain numberof factors that determine its outcome. InMLR technique, thereis one dependent variable to be predicted and two or moreindependent variables in the general form of MLR can beexpressed as follows:

Y ¼ b1 þ b2 X 2 þ…………þ bk X k þ e; ð4Þ

where Y (visibility) is dependent variable, X2, X3 … , Xk

(previous day's visibility, air pollutants, and meteorologicalvariables) are independent variables, b1, b2 … , bk are linearregression parameters, e is an estimated error term which isobtained from independent random sampling from the normaldistribution with mean zero and constant variance. The task ofregression modeling is to estimate the regression parametersb1, b2 … , bk,, which can be obtained using the least squaretechnique.

Equation (4) can be written in this form

Y ¼ X bþ e

where Y ¼

Y 1

Y 2

::Yn

266664

377775; X ¼

1X 21X 31…:X k1

…: ::1X 2n X 3n…:X kn

24

35;

b ¼

b1b2::bk

266664

377775and e ¼

e1e2::en

266664

377775

ð5Þ

So Y is an n x 1, X is an n x k, b is a k x 1 and e is an n x 1matrix.

After using the least square technique, the solution can beobtained as b =(X ′X)−1(X ′Y ), X ′ is the transpose of a matrixX . The resulting model can be used to forecast futureobservations.

But when multicollinearity is present in the data, the com-putation of a matrix inverse ((X ′X)−1) becomes dubious. Thislimitation is removed by applying the PCA. It is also usefulwhen a large number of variables are obtained and they arecorrelated with each other. The application of PCA with aregression model aims to reduce the collinearity of thedatasets, which leads the worst predictions and determinethe relevant independent variables for the prediction [28].There is a noticeable difference in input data of PCR andMLR as independent parameters go directly to the MLR,whereas PC obtained from independent parameters are usedas input to PCR.

Computation of PCs

PCs have been computed by the covariance of the input datamatrix. The eigenvalues of the covariance matrix “C” areobtained from its characteristic equation:

C−λIj j ¼ 0 ð6Þ

where, λ is the eigenvalue and I is the identity matrix.

136 P. Goyal et al.

For each eigenvalue, a non-zero vector e is defined as

C e ¼ λe; ð7Þ

where the vector e is called the characteristic vector or eigen-vector of the covariance matrix C associated with its corre-sponding eigenvalue. The eigenvectors derived from the co-variance matrix represent the mutually orthogonal linear com-bination of the matrix. Their associated eigenvalue representsthe amount of total variance, which is explained by each of theeigenvectors. By retaining only the first few pairs of eigen-value–eigenvector, or PCs, a substantial amount of the totalvariance can be explained. The higher-order PCs, which ex-plain minimal amounts of the total variance, can be viewed asnoise. The variance explained by i th PC is expressed as:

Variancei ¼ λiXn

λn

ð8Þ

The PC, associated with the greatest eigenvalue, the firstPC (PC1), represents the linear combination of the vari-ables, accounting for the maximum total variability in thedata. The second PC, explains the maximum variability, isnot accounted by the PC1 and so on. All components, thatcumulative variance approximately 85 %, are selected inthe present study. The rest of the components, that explainless variance than any of the original variables, are ignored.After getting the PCs, the initial data set is transformed intothe orthogonal set by multiplying the eigenvectors to theinitial data set. Now this transformed data set is used asinput to the MLR technique.

Y ¼ β0 þ β1 PC1ð Þ þ β2 PC2ð Þ þ………………þ βn PCnð Þ þ e;

ð9Þ

where β0, β1, β2, … βn are the coefficients in the modelequation. The coefficients of regression model have beenestimated using the method of least square. The resultingmodel can be used to forecast future observations.

The statistical measures, which have been used for statisti-cal evaluation of the performance of models has been given byChang and Hanna [29].

References

1. Seinfeld, J., & Pandis, S. (1998). Atmospheric chemistry and physics:from air pollution to climate change (2nd ed.). Hoboken, NewJersey: Wiley.

2. Tang, I. N. (1997). Thermodynamic and optical properties of mixed-salt aerosols of atmospheric importance. Journal of GeophysicalResearch, 102 , 1883–1893.

3. Lee, C. T., & Tsai, J. J. (1998). Aerosol light-scattering coefficientsand size distributions in a suburban area in Taiwan. Journal ofAerosol Science, 29, S651–S652.

4. La Roche, P. (2011). Carbon-neutral architectural design. BocaRaton: CRC Press.

5. Brimblecombe, P. (1981). Long term trends in London fog. Scienceof the Total Environment, 22, 19–29.

6. Tsai, Y. I. (2005). Atmospheric visibility trends in an urbanarea in Taiwan 1961–2003. Atmospheric Environment, 39 ,5555–5567.

7. Economic Survey of Delhi (2008–2009). Minister for finance andplanning. Delhi: Government of Delhi, India.

8. Byun, D.W., & Ching, J. K. S. (1999). Science algorithms of the EPAModels-3 Community Multiscale Air Quality (CMAQ) modelingsystem, EPA/600/R-99/030. Office of Research and Development .Washington, DC: U.S. Environmental Protection Agency.

9. Boutahar, J., Lacour, S., Mallet, V., Queolo, D., Roustan, Y., &Sportisse, B. (2004). Development and validation of a fully modularplatform for numerical modelling of air pollution: POLAIR. Interna-tional Journal of Environmental Pollution, 22, 17–28.

10. Chelani, A. B., Rao, C. V. C., Phadke, K. M., & Hasan, M. Z.(2002). Prediction of sulphur dioxide concentration using ar-tificial neural networks. Environmental Modelling and Soft-ware, 17 , 161–168.

11. Ziomas, I. C.,Melas, D., Zerefos, C. S., Bais, A. F., & Paliatsos, A. G.(1995). Forecasting peak pollutant levels from meteorological vari-ables. Atmospheric Environment, 29 , 3703–3711.

12. Polydoras, G. N., Anagnostopoulos, J. S., & Bergeles, G. (1998). Airquality predictions: dispersion model vs Box–Jenkins stochasticmodels. An implementation and comparison for Athens, Greece.Applied Thermal Engineering, 18 , 1037–1048.

13. Robeson, S. M., & Steyn, D. G. (1990). Evaluation and comparisonof statistical forecast models for daily maximum ozone concentra-tions. Atmospheric Environment, 24B , 303–312.

14. Shi, J. P., & Harrison, R. M. (1997). Regression modelling of hourlyNOx and NO2 concentrations in urban air in London. AtmosphericEnvironment, 31, 4081–4097.

15. Comrie, A. C. (1997). Comparing neural networks and regressionmodels for ozone forecasting. Journal of the Air and Waste Manage-ment Association, 47, 653–663.

16. Cogliani, E. (2001). Air pollution forecast in cities by an air pollutionindex highly correlated with metrological variables. AtmosphericEnvironment, 35, 2871–2877.

17. Chan, Y. C., Simpson, R. W., Mctainsh, G. H., Vowles, P. D., Cohen,D. D., & Bailey, G. M. (1999). Source apportionment of visibilitydegradation problems in Brisbane (Australia) using the multiplelinear regression techniques. Atmospheric Environment, 33 , 3237–3250.

18. Kumar, A., & Goyal, P. (2012). Forecasting of air quality in Delhiusing principal component regression technique. Atmospheric Pollu-tion Research, 2 , 436–444.

19. Central Pollution Control Board. (2005). PARIVESH highlights2004. Delhi: CPCB.

20. Lalas, D., Veirs, V. R., Karras, G., &Kallos, G. (1982). An analysis ofthe SO2 concentration in Athens, Greece. Atmospheric Environment,24 , 3703–3711.

21. Singh, S., Nath, S., Kohli, R., & Singh, R. (2005). Aerosols overDelhi during pre-monsoon months: characteristics and effects onsurface radiation forcing. Geophysical Research Letters, 32 ,L13808. 4 PP.

22. Schichtel, B. A., & Husar, R. B. (2001). Eastern North Americantransport climatology during high and low-ozone days. AtmosphericEnvironment, 35, 1029–1038.

23. Husar, R. B., Husar, J. D., & Martin, L. (2000). Distribution ofcontinental surface aerosol extinction based on visual range data.Atmospheric Environment, 34, 5067–5078.

Impact of Air Pollutants and Meteorological Variables 137

24. Sarkar, P.K., Bose, S., & Ghose, P. (2007) A critical appraisal oftraffic and transportation sector meeting in Delhi and possible solu-tions. Paper no. 532.

25. Delhi Sattistical Handbook (2012). http://www.delhi.gov.in/wps/wcm/connect/doit_des/DES/Our+Services/Statistical+Hand+Book/.

26. Gokhale, S., & Pandian, S. (2007). A semi-empirical box model-ing approach for predicting the carbon monoxide concentration atan urban traffic intersection. Atmospheric Environment, 41 ,7940–7950.

27. Chung, M. K. (2007). Correlation coefficient. In N. J. Salkin (Ed.),Encyclopedia of measurement and statistics (Vol. 1, pp. 189–191).London, UK: Sage Publications, Print.

28. Sousa, S. I. V., Martins, F. G., Alvim-Ferraz, M. C.M., & Pereira, M.C. (2007). Multiple linear regression and artificial neural networksbased on principal components to predict ozone concentrations.Environmental Modelling & Software, 22 , 97–103.

29. Chang, J. C., & Hanna, S. R. (2004). Air quality model performanceevaluation. Meteorology and Atmospheric Physics, 87 , 167–196.

138 P. Goyal et al.