Atmospheric Pollution Research

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1 AtmosphericPollutionResearch2(211) Atmospheric Pollution Research ForecastingofairqualityinDelhiusingprincipalcomponent regressiontechnique AnikenderKumar,PramilaGoyal CentreforAtmosphericSciences,IndianInstituteofTechnologyDelhi,HauzKhas,NewDelhi116India ABSTRACT Overthepastdecade,anincreasinginteresthasevolvedbythepublicintheday to dayairqualityconditionsto which they are exposed. Driven by the increasing awareness of the health aspects of air pollution exposure, especiallybymostsensitivesub populationssuchaschildrenandtheelderly,short termairpollutionforecasts are being provided more and more by local authorities. The Air Quality Index () is a number used by governmentalagenciestocharacterizethequalityoftheairatagivenlocation.isusedforlocalandregional airqualitymanagementinmanymetropolitancitiesoftheworld.themainobjectiveofthepresentstudyisto forecast short term daily through previous day s and meteorological variables using principal componentregression(pcr)technique.thisstudyhasbeenmadeforfourdifferentseasonsnamelysummer, monsoon,postmonsoonandwinter.wasestimatedfortheperiodofsevenyearsfrom2 26atITO(a busiesttrafficintersection)forcriteriapollutantssuchasrespirablesuspendedparticulatematter(rspm),sulfur dioxide (SO 2 ), nitrogen dioxide (NO 2 ) and suspended particulate matter (SPM) using a method of US EnvironmentalProtectionAgency(USEPA),inwhichsub indexandbreakpointpollutantconcentrationdepends onindiannationalambientairqualitystandard(naaqs).theprincipalcomponentshavebeencomputedusing covarianceofinputdatamatrix.onlythosecomponents,havingeigenvalues1,wereusedtopredictthe usingprincipalcomponentregressiontechnique.theperformanceofpcrmodel,usedforforecastingof, was better in winter than the other seasons as studied through statistical error analysis. The values of normalizedmeansquareerror(nmse)werefoundas.58,.82,.241and.418forwinter,summer, postmonsoonandmonsoonrespectively.theotherstatisticalparametersarealsosupportingthesameresult. Keywords: Forecasting Principalcomponentregression(PCR) Airqualityindex() Meteorologicalvariables Pollutants ArticleHistory: Received:3November21 Revised:2February211 Accepted:8February211 CorrespondingAuthor: PramilaGoyal Tel: Fax: pramila@cas.iitd.ernet.in Author(s)211.ThisworkisdistributedundertheCreativeCommonsAttribution3.License. doi:1.594/apr Introduction With continuous development and increase of population in theurbanareas,aseriesofproblemsrelatedtoenvironmentsuch 1975;AronandAron,1978;Lin,1982;Aron,1984;Katsoulis,1988; RobesonandSteyn,199).Manyofthepreviousstudies(Sanchez et. al., 199; Mantis et al., 1992; Milionis and Davies, 1994) analyzed the meteorological conditions associated with high asdeforestation,releaseoftoxicmaterials,solidwastedisposals, pollutant concentrations. These studies usually produced air pollution and many more, have attracted attention much greaterthaneverbefore.theproblemofairpollutionincitieshas becomesoseverethatthereisaneedfortimelyinformationabout changes in the pollution level. Today forecasting of air quality is oneofthemajortopicsofairpollutionstudiesduetothehealth effectscausedbytheseairbornepollutantsinurbanareasduring pollution episodes. Therefore, the development of effective forecastingmodelsofformajorairpollutantsinurbanareasis ofprimeimportance.withthisendinview,thereisaneedtohave a model that would generate the future. Although many forecastingmodelsexistandsomeareinuse,thereisstillneedfor developingmoreaccuratemodels.thegaussiandispersionmodels aregenerallyusedinmostoftheairpollutionstudies.eventhough the models have some physical basis, detailed information about thesourceofthepollutantsandothervariablesaregenerallynot known. In order to overcome these limitations, statistical models are used, which facilitate the prediction of pollutant concen trations(finziandtebaldi,1982;ziomassetal.,1995;polydoraset al.,1998). Numerousstudiesbasedonthestatisticalmodelshavebeen carried out in different regions to identify local meteorological conditions, most strongly associated with air pollutant concen trations, and to forecast their values (McCollister and Willson, qualitative or semi quantitative results and shed a light on the relation between the meteorological conditions and pollutant concentrations. Shi and Harrison (1997) developed a regression model for the prediction of NO x and NO 2 in London. Some non linear models i.e., Artificial Neural Networks can also be used to forecastthepollutantconcentrations(boznaretal.,1993;comrie, 1997). Asforthehealthimpactofairpollutants,isanimportant indicatorforgeneralpublictounderstandeasilyhowbadorgood theairqualityisfortheirhealthandtoassistindatainterpretation for decision making processes related to pollution mitigation measures and environmental management. Basically, the is defined as an index or rating scale for reporting daily combined effect of ambient air pollutants recorded in the monitoring sites. Recently,VandenElshoutetal.(28)gaveareviewofexistingair quality indices and a proposal of a common alternative. Fuzzy inferencesystemshavealsousedinmodelingofairqualityindices by Hajek and Olej (29). A regression model was also used by Cogliani(21)forairpollutionforecastincitiesbyanairpollution index highly correlated with meteorological variables. However, when multicollinearity is present, the computations of regression coefficients in regression models become dubious. Principal componentanalysis(pca)canbeappliedtoovercometheabove

2 KumarandGoyal AtmosphericPollutionResearch2(211) limitation. PCA is also a procedure to reduce the number of variables.itisusefulwhenobtaineddatahasanumberofvariables (possibly a large number of variables), and believed that there is somevariablesthosearecorrelatedwithoneanother.sanchezet al.(1986)usedtheprincipalcomponentfactoranalysisforstudying thespatialandtemporaldistributionofso 2 inanurbanarea.the PCR technique was also used to forecast the long range forecastingofsouthwestmonsoonrainfalloverindia(rajeevanet al.,25).themostoftheairqualityforecastingindelhihasbeen done through individual air pollutants whereasthepresentstudy was conducted using principal component regression technique with respect to daily. The PCR model is used in the present studytoforecastthedailyairqualityindexonedayinadvance. 1.1.Descriptionandmeteorologyofstudyarea TheDelhicity(Latitude28 35'N,Longitude77 12'E)islocated inthenorthernpartofindiaandsituatedbetweenthegreatindian Desert (Thar Desert) of Rajasthan to the west, the central hot plains to the south and the cooler hilly region to the north and east.delhihasasemi aridclimatewithanextremelyhotsummer, average rainfall and very cold winter. Due to the worst meteorological scenario, the most important season in Delhi is winter,whichstartsindecemberandendsinfebruary.thisperiod isdominatedbycold,dryairandground basedinversionwithlow windconditions(u1ms 1 ),whichoccurfrequentlyandincreases theconcentrationofpollutants(anfossietal.,199).thesummer (March, April, May) is governed by high temperature and high winds, while the monsoon (June, July, August) is dominated by rains and post monsoon (September, October, November) has moderatetemperatureandwindconditions. Delhi, the capital city of India with 13.8 million inhabitants spreadover1483km 2 (Anejaetal.,21).Duetothepresenceof large number of industries and migration of people from neighboringstates,nearly5.4millionvehiclesarerunningondelhi roads.theemissionofpollutantsfromthesesourcesdeteriorates theambientairquality.thesteepincreaseinvehicularpopulation (major source of air pollution) has resulted in corresponding increase in pollutants emitted by these vehicles. Presently, more than13tonsofpollutantsareemittedbythevehiclesindelhi. Due to the increased level of pollutants, Delhi s air is blamed for 4%ofemergencyhospitaladmissionsofpatientswithbreathing and heart complaints. The ambient air quality data of Delhi monitored by Central Pollution Control Board (CPCB) shows very highvaluesofsuspendedparticles,so 2 andno x whichhavebeen beyondthepermissiblelimitsfromlastseveralyearscontinuously (GoyalandSidhartha,23).AllIndiaInstituteofMedicalSciences (AIIMS)reportsthattherewasamassive9%increaseinasthma cases in December 1999 compared to December Study by Brandon and Hommann (1995), by using the standard US metric, estimated that the 749 deaths could be avoided in Delhi by a μg m 3 reduction in PM 1. One, out of every 1 school childreninthecity,suffersfromasthmathatisworseningdueto vehicularairpollution. Theprimaryobjectiveofthisstudyistoforecastthedaily onedayinadvanceonseasonalbasis.abusiesttrafficintersection ITO has been chosen to forecast using the air pollutant concentrationsmonitoredatito,sinceitisacontinuousairquality monitoring station at the same place. The daily air quality parameters (daily average concentrations of pollutants) namely RSPM,SO 2,NO 2 andspmusedinthepresentstudyweremeasured bycpcb,aregulatorymonitoringagencyindelhi.thelocationsof monitoring stations were categorized on a land use basis (CPCB, 25) i.e., residential, industrial and traffic intersections. The stationthatisclassifiedastrafficintersectionisito.inthisstudy, was calculated using USEPA method in which sub index and breakpointpollutantconcentrationsdependonindiannaaqsand apcrtechniquewasalsousedtoforecasttheshorttermi.e.,daily throughpreviousday sandmeteorologicalvariables. The 24 hourly averaged surface meteorological variables at Safdarjung airport like daily maximum temperature (t max ), minimum temperature (t min ), daily temperature range (difference between daily maximum and minimum temperature, t range ), averagetemperature(t avg ),windspeed(wsp),winddirectionindex (wdi), relative humidity (rh), vapor pressure (vp), station level pressure (slp), rainfall (rf), sunshine hours (ssh), cloud cover (cc), visibility (v) and radiation (rd) for Delhi were acquired from the Indian Meteorological Department (IMD), Pune for the period of There is no meteorological station at ITO. The meteorologicalstationisatsafdarjungairportabout5.7kmfrom theitoandthisistheonlystationinthestudyarea(ito).figure1 shows the air pollution monitoring (ITO) and meteorological (Safdarjungairport)stationsontheMapofDelhi. 2.MaterialsandMethods Thereareprimarilytwostepsinvolvedinformulatingan: first the formation of sub indices of each pollutant, second the aggregation (breakpoints) of sub indices. Breakpoint concen trationsofeachpollutant,usedincalculationof,arebasedon IndianNAAQSandresultsofepidemiologicalstudiesindicatingthe risk of adverse health effects of specific pollutants. It has been noticedthatdifferentbreakpointconcentrationsanddifferentair qualitystandardshavebeenreportedinliterature(environmental Protection Agency, 1999). In India, to reflect the status of air qualityanditseffectsonhumanhealth,therangeofindexvalues has been designated as Good ( ), Moderate (11 2), Poor(21 3), VeryPoor(31 4) and Severe(41 5) (Table1)(Nagendraetal.,27). AllthevaluesofSO 2,NO 2,RSPMandSPMareinμgm 3. Theformula(EPA,1999)usedtocalculateforfourcriteria pollutants RSPM, SO 2, NO 2 and SPM from 2 26 is given below: IHi I Lo IP C P BPLo ILo (1) BP BP Hi Lo where I P is the for pollutant p, C P is the actual ambient concentrationofthepollutant p,bp Hi isthebreakpointintable1 thatisgreaterthanorequaltoc p,bp Lo isthebreakpointintable1 that is less than or equal to C p, I Hi is the sub index value correspondingtobp Hi,and,I Lo isthesubindexvaluecorresponding tobp Lo. Theisdeterminedonthebasisofofstudypollutants and the highest among them is declared as the overall. The formulausedhereissameasusedbyusepa,inwhichsubindex andbreakpointconcentrationdependsonindiannaaqs Multiple Linear Regression and Principal Component Regressionmodel Aforecastcanbeexpressedasafunctionofacertainnumber of factors that determine its outcome. Multiple linear regression (MLR)techniqueincludesonedependentvariabletobepredicted andtwoormoreindependentvariables.ingeneral,multiplelinear regressioncanbeexpressedasinequation(2): Y=b 1 +b 2 X b k X k +e (2)

3 438 KumarandGoyal AtmosphericPollutionResearch2(211) N Safdarjung ITO(Airqualitymonitoringstation) Safdarjung(Meteorologicalstation) Figure1.MapofDelhiwithairpollutionmonitoring(ITO)andmeteorological(Safdarjungairport)stations(Source: Table1.ProposedsubindexandbreakpointpollutantconcentrationsforIndian SI.No. Indexvalues Descriptor SO 2 (24havg.) NO 2 (24havg.) RSPM(24havg.) SPM(24havg.) 1 Good a Moderate b Poor c VeryPoor d Severe e >1572 >1272 >42 >8 a Good:Airqualityisacceptable;however,forsomepollutantstheremaybeamoderatehealthconcernforaverysmall numberofpeople. b Moderate:Membersofsensitivegroupsmayexperiencehealtheffects. c Poor:Membersofsensitivegroupsmayexperiencemoreserioushealtheffects. d Verypoor:Triggershealthalter,everyonemayexperiencemoreserioushealtheffects. e Severe:Triggershealthwarningsofemergencyconditions. where Y is the dependent variable, X 2, X 3..., X k are the independent variables, b 1, b 2...,b k are linear regression parameters. In this model, is the dependent variable and, previousday sandmeteorologicalvariables,areindependent variables, e is an estimated error term which is obtained from independent random sampling from the normal distribution with meanzeroandconstantvariance.thetaskofregressionmodeling is to estimate the b 1, b 2...,b k, which can be done using minimumsquareerrortechnique. Equation(2)canbewritteninthefollowingform: ( Y=Xb+e (3) where Y1 b1 e1 Y2 1 X21 X31... X k1 b2 e2 Y= :,X=.....,b= : ande= : : 1 X2n X3n... X kn : : Y n b k e n SoYisannx1,Xisannxk,bisakx1andeisannx1matrix. Afterusingtheminimumsquareerrortechnique,thesolution canbeobtainedasb=(x X) 1 (X Y).Further,theF testhasbeen performedtodeterminewhetherarelationshipexistsbetweenthe dependentvariableandtheregressors.thet testisperformedin order to determine the potential value of each of the regressor variablesintheregressionmodel.theresultingmodelcanbeused topredictfutureobservations. When multicollinearity is present the computation of an inverse matrix (X X) 1 becomes dubious. PCA can be applied to overcome this limitation. It is useful when large number of variables are present, and also if there are some variables correlatedwitheachother. TheapplicationofPCAwithregressionmodelaimstoreduce thecollinearityinthedatasetswhichleadstotheworstpredictions and also determine the relevant independent variables for the predictionofairpollutantconcentrations(sousaetal.,27).the differencebetweenpcrandmlrismainlyduetoinputdata.pcr model takes PCs of variables as input data and reduces the complexityduetolessnumberofinputvariables. Computationofprincipalcomponents.Principalcomponentscan becomputedbycovarianceofinputdatamatrix.inthisstudy,the covariance matrix of the initial data was considered. The

4 KumarandGoyal AtmosphericPollutionResearch2(211) eigenvalues of the covariance matrix C are obtained from its characteristicequation: CI (4) where, istheeigenvalueandiistheidentitymatrix. Foreacheigenvalue,anon zerovectorecanbedefinedas: Cee (5) wherethevectoreiscalledthecharacteristicvectororeigenvector of the covariance matrix C associated with its corresponding eigenvalue. The eigenvectors derived from the covariance matrix represent the mutually orthogonal linear combination of the matrix.theirassociatedeigenvaluerepresenttheamountoftotal variance, which is explained by each of the eigenvectors. By retaining only the first few pairs of eigenvalue eigenvector, or principal components, a substantial amount of the total variance can be explained while explaining the higher order principal componentswhichexplainminimalamountsofthetotalvariance andcanbeviewedasnoise.varianceexplainedbyi th PCisgiven by: i Thevariancei (6) n n The PC associated with the greatest eigenvalue, the first PC (PC1), represents the linear combination of the variables accounting for the maximum total variability in the data. The secondpcexplainsthemaximumvariabilitythatisnotaccounted bythepc1andsoon.allcomponentswitheigenvalues>1should beretained.therationalebehindthismethodisaneigenvalueof 1, represents amount of variance, explained by the original variables, and components of eigenvalue<1 explain less variance than the original variables. After getting the PC s, the initial data set is transformed in to the orthogonal set by multiplying the eigenvectorstotheinitialdataset.nowthistransformeddataset isusedasinputtothemultiplelinearregressiontechnique. Y 1(PC 1) 2(PC 2)... n(pc n) e (7) where, 1, 2 n arethecoefficientsinthemodelequation. The coefficients of regression model have been estimated using theleastsquaresmethod.further,thef testhasbeenperformed todeterminewhetherarelationshipexistsbetweenthedependent variable and the regressors. The t test is performed in order to determinethepotentialvalueofeachoftheregressorvariablesin theregressionmodel.theresultingmodelcanbeusedtopredict futureobservations. PrincipalComponentswerecomputedusingthedataforthe years2 25andalsousedasaninputtoregressionmodelto form PCR model. The same process was adopted for all four seasons.thepreviousday sandmeteorologicalvariables(15 variables,asmentionedinsection1)fortheyears2 25were usedastheinputtopcrmodel.thecovariancematrixofthegiven inputisdetermined.thepcshavebeendeterminedonthebasisof thevarianceexplainedbytheeigenvaluesofthecovariancematrix. Onlythoseprincipalcomponentswhoseeigenvalues1basedon the analysis of 15 variables, were used to forecast one daily air quality index. The application of PCA with regression models reduces the collinearity of the datasets, which can lead to worst predictions and also determines the relevant independent variables for the prediction of. The architecture of the PCR modeltoforecasthasbeenshowninfigure2.thedifference between the PCR and MLR is due to the input variables. Consequently,thenetworkarchitecturewillbelesscomplexinPCR duetothedecreasednumberofinputvariables. Once this process has been completed, the performance of PCRmodelhasbeenvalidatedwithanindependentdata,observed fortheyear26,thathasbeentransformedtothenewdataset usingthepreviouslydeterminedweightsofprincipalcomponents. Itisimportanttomentionthat26datawasnotusedtobuildthe model. The accuracy of the model was analyzed through the statisticalparameters. 3.ResultsandDiscussion Theforecastingofdaily,basedonpreviousday sand meteorologicalvariables,wasdoneusingmlrandpcrmodelon the seasonal basis for the period of 2 25 and validated throughthedailyof26. The regression models for different seasons, summer, monsoon, post monsoon and winter were developed using the MLRtechniqueonthebasisofdailydataof2 25usingthe procedurediscussedinsection2.theregressionequationsbased onmlrtechniqueareobtainedasequations(8),(9),(1)and(11) for summer, monsoon, post monsoon and winter season, respectively. Figure2.ArchitectureofPCRmodelfortheforecastingof.

5 44 KumarandGoyal AtmosphericPollutionResearch2(211) [] [ d1].462 [rh] (8) [t max] [cc] [] [ d1] [rh] (9) [v] 3.44 [t min] [] [ d1] 1.72 [slp] (1) 1.67 [vp] [ssh] 2.49[v] 1.49[t max] [] [ d1] 15.6 [v] (11) 7.98 [cc] 4.5 [wsp] 1.19[rh].84[rf] Equations(8) (11)showthatpreviousday sairqualityindexis thecommonvariableforallseasons. Thedailyoftheyear26hasbeenforecastedusingthe aboveequations,whichhasbeencomparedwithobservedof 26. The statistical evaluation of forecasted and observed valuesisshownintable2.resultsindicatedthatthemlrmodelis performing satisfactorily in all seasons and gives better results in winter with respect to the NMSE and Root Mean Square Error (RMSE).Itshowsaminordifferenceincoefficientofdetermination compared to the other seasons. Fractional bias shows that the modelisunder predictinginsummer,postmonsoonandwinterin trainingaswellasinvalidationandisover predictinginmonsoon season. The PCR models for summer, monsoon, post monsoon and winter, based on the daily data for the years 2 25 were developedasdiscussedinsection2andwereanalyzedstatistically. As a first step, data for the years 2 25 was used to calculatethecovariancematrixforallfourseasons.thepredictor variablesweretransformedintoprincipalcomponentsthroughthe eigenvaluematrixofvariablesthatwouldexplainmostofthetotal variation in the data. Table 3 represents the eigenvalues and amount of variance, explained by each principal component with eigenvalues1. Rest of the components having eigenvalues<1, explaininglessvariancethananyoforiginalvariableswereignored. Table 3 also shows that only 5 PCs have eigenvalues1 with a cumulative variance of in summer and 4 PCs have eigenvalues1withcumulativevariancesof6.79,68.35and66.62 in monsoon, post monsoon and winter, respectively. Communalities of each original variable in all four seasons are shown in Table 4, using the first 5 PCs in summer and 4 PCs in monsoon, post monsoon and winter seasons. This Table reflects thatthemostrelevantoriginalvariablesforpcrareaveragedaily temperature, relative humidity, daily minimum temperature and daily average temperature in summer, monsoon, post monsoon andwinter,respectively. Table2.ComparisonofMLRmodelpredictedandobservedvaluesinyears225andyear26 S.N. Season RMSE NMSE Coefficientof determination Fractional Bias RMSE NMSE Coefficientof determination Fractional Bias 1 Summer Monsoon PostMonsoon Winter Table3.EigenvaluesandexplainedvarianceofthecomputedPCsforsummer,monsoon,postmonsoonandwinterseasons Seasons Summer Monsoon Post monsoon Winter Principal Component Eigenvalue %ofvariance Cumulative variance(%)

6 KumarandGoyal AtmosphericPollutionResearch2(211) Table 4. Communalities of each original variable for summer, monsoon, postmonsoonandwinterseasons Variable Summer Monsoon Post Monsoon Winter d t avg rh vp rf wsp wdi rd t max t min ssh slp v cc t range The loadings (or coefficients) of each input variable correspondingtoall5pcsinsummerand4pcsinmonsoon,post monsoon and winter are given in Tables S1, S2, S3 and S4, respectively(seethesupportingmaterial,sm).inthiscase,only5 new variables (PCs) were used instead of original 15 variables in (a) summer and 4 new variables were used for the remaining three seasons. ThePCRmodelsforallfourseasonsbasedonthetransferred datafor2 25weredevelopedandanalyzedstatistically.The T test was used to test the significance of the variables. Insignificant/statisticallyinvalidvariableswereremovedfromthe modelequation.itwasobservedthat3pcs(pc1,pc2andpc3)lied in95%confidenceintervalandthesevariableswereretainedinthe modelequations.itwasalsoobservedthattwopcs(pc1andpc2), one PC (PC1) and two PCs (PC2 and PC4) lied in 95% confidence intervalinmonsoon,postmonsoonandwinter,respectively.thus, theforecastingequations(12,13,14,and15)usingpcrtechnique forfourseasonsareshownbelow: [] PC1 1.4PC2.969PC3 [] PC1.398PC2 [] PC1 (12) (13) (14) [] PC2.617PC4 (15) Figures3a,3b,3c,and3dshowgraphicalpresentationoffour different seasons. The coefficient of correlation (R) between observed and forecasted values for the years 2 25 were found as.7,.79,.8 and.64 in summer, monsoon, post monsoonandwinter,respectively.thedailyoftheyear26 wasforecastedusingtheequations(12) (15). (b) Ovserved (c) (d) Figure3.Comparisonofobservedandmodelpredictedvaluesofdailyin(a)Summer,(b)Monsoon, (c)postmonsoonand(d)winterseasonsduringtheyears

7 442 KumarandGoyal AtmosphericPollutionResearch2(211) Thecomparisonofforecastedandobservedvaluesforthe year 26 are shown in Figures4a, 4b, 4c, and 4d for summer, monsoon,postmonsoonandwinter,respectively.figures3and4 showthatmaximumobservedis497andtheminimumis48in monsoon season of 23 and 2 respectively, whereas the predicted maximum is 447 and the minimum is 96.5 in monsoonfortheperiodsof23and2.theobservedvalues for26werenotincludedinmodeldevelopmentforforecasting of 26. Figure 4 also shows that there is one day shifting betweenthepredictedandobservedvaluesof.thereasonfor this shifting may be due to the uncertainties involved in the air qualitydatafortheyears2 25thatwasvalidatedwiththe datafor26. Statisticalevaluationbetweenobservedandpredictedvalues for2 25and26wasmadefordifferentseasonsinTable5. The NMSE and coefficient of determination (R 2 ) are found as (.82,.5767) in summer, followed by (.418,.4225) in monsoon;(.241,.5155)inpostmonsoonand(.58,.5625) in winter seasons during 26.This shows that forecasted could be explained by the selected input variables as approximately 58% in summer, 57% in winter, 52% in post monsoonand42%inmonsoonseasons.fractionalbiasshowsthe (a) under predictionofpcrmodelinalltheseasonsintrainingaswell as in validation. However, the overall performance of the PCR modelwasfoundbetterincomparisontothemlrmodelandalso model sperformancewasfoundtobebetterinwintercompared tootherseasons. 4.Conclusions Inthepresentstudy,thedailyatITOwasforecastedusing the MLR and PCR models based on the previous day s and meteorologicalvariables. Thestatisticallyerroranalysisofmodelevaluationforallfour seasons shows that model is performing satisfactorily in all the seasonsbutisperformingbetterinwinterthantheotherseasons. TheuseofPCsbasedmodelswasfoundusefulduetoelimination of collinearity problems in MLR and reduction of the number of predictors.itisalsofoundthattheperformanceofthepcrmodel was found better in comparison to the MLR model in 26 validationperiod.finally,itcouldbeconcludedthattheairquality forecastingwouldbehelpfultoconcernedauthoritiesinproviding the necessary information to the general public, to protect their healthandtakenecessaryprecautionarymeasures. (b) (c) (d) Figure4.Comparisonofobservedandmodelpredictedvaluesofdailyin(a)Summer,(b)Monsoon, (c)postmonsoonand(d)winterseasonsduringtheyear26. Table5.ComparisonofPCRmodelpredictedandobservedvaluesinyears225andyear26 S.N. Season RMSE NMSE Coefficientof determination Fractional Bias RMSE NMSE Coefficientof determination Fractional Bias 1 Summer Monsoon Post Monsoon Winter

8 KumarandGoyal AtmosphericPollutionResearch2(211) Appendix Thestatistical measuresusedforstatisticalevaluationofthe performanceofmodelsweregivenbychangandhanna(24)as follows: Coefficient of Correlation (R). Coefficient of correlation (R) is relative measure of the association between the observed and predicted values. It can vary from (which indicates no correlation)to+1.(whichindicatesperfectcorrelation).avalueof Rcloseto1.impliesgoodagreementbetweentheobservedand predictedvalues,i.e.goodmodelperformance. R CoCoCpCp C p C o Coefficient of Determination (R 2 ). Coefficient of determination (R 2 ),whichisthesquare of coefficient of correlation, determines theproportionofvariancethatcanbeexplainedbythemodel. Root Mean Square Error (RMSE). RMSE, is a measure of the differencesbetweenvaluespredictedbyamodelandtheobserved valuesandisexpressedasfollows: 2 o p RMSE C C Normalized Mean Square Error (NMSE). NMSE, as a measure of performance,emphasizesthescatterintheentiredatasetandis definedasfollows: NMSE C 2 ocp C.C o p The normalization by C.C o p ensures that NMSE will not be biasedtowardsmodelsthatover predictorunder predict.ideal value for NMSE is zero. Smaller values of NMSE denote better modelperformance. Fractional Bias (FB). It is a performance measure known as the normalizedorfractionalbiasofthemeanconcentrations: Co CP FB.5 C o C P where C p are the model predictions, C o are the observations, Overbar C is the average over the dataset, and C is the standarddeviationoverthedataset. SupportingMaterialAvailable The weights of the PC s for summer season (Table S1), The weightsofthepc sformonsoonseason(tables2),theweightsof thepc sforpostmonsoonseason (Table S3), The weightsofthe PC sforwinterseason(tables4).thisinformationisavailablefree ofchargeviatheinternetathttp:// References Aneja,V.P.,Agarwal,A.,Roelle,P.A.,Phillips,S.B.,Tong,Q.S.,Watkins,N., Yablonsky,R.,21.Measurementsandanalysisofcriteriapollutants innewdelhi,india.environmentinternational27,3542. Anfossi, D., Brisasca, G., Tinarelli, G., 199. Simulation of atmospheric diffusioninlowwindspeedmeanderingconditionsbyamontecarlo dispersionmodel.ilnuovocimento13c,9956. Aron, R., Models for estimating current and future sulphur dioxide concentrationsintaipei.bulletinofgeophysics25, Aron, R., Aron, I. M., Statistical forecasting models: I. Carbon monoxide concentrations in the Los Angeles basin. Journal of Air PollutionControlAssociation28, Boznar,M.,Lesjak,M.,Mlakar,P.,1993.Aneuralnetworkbasedmethod for shortterm predictions of ambient SO 2 concentrations in highly pollutedindustrialareasofcomplexterrain.atmosphericenvironment PartBUrbanAtmosphere27, Brandon, C., Hommann, K., The cost of inaction: valuing the economywidecostofenvironmentaldegradationinindia.proceedings ofthesymposiumonglobalsustainability,unitednationsuniversity, Tokyo. Central Pollution Control Board, 25. PARIVESH highlights 24Delhi: CPCB. Chang, J.C., Hanna, S.R., 24. Air quality model performance evaluation. MeteorologyandAtmosphericPhysics87, Cogliani, E., 21. Air pollution forecast in cities by an air pollution index highly correlated with meteorological variables. Atmospheric Environment35, Comrie,A.C.,1997.Comparingneuralnetworksandregressionmodelsfor ozone forecasting. Journal of the Air and Waste Management Association47, EPA,1999.AirQualityIndexReporting;FinalRule,FederalRegister,PartIII, 4CFRPart58. Finzi,G.,Tebaldi,G.,1982.Amathematicalmodelforairpollutionforecast andalarminanurbanarea.atmosphericenvironment16, Goyal, P., Sidhartha, 23. Present scenario of air qualityin Delhi: a case study of CNG implementation. Atmospheric Environment 37, Hajek, P., Olej, V., 29. Air quality indices and their modelling by hierarchical fuzzy inference systems. WSEAS Transactions on EnvironmentandDevelopment1, Katsoulis, B.D., Some meteorological aspects of air pollution in Athens,Greece.MeteorologyandAtmosphericPhysics39, Lin, G.Y., Oxidant prediction by discriminant analysis in the south coastairbasinofcalifornia.atmosphericenvironment16, Mantis,H.T.,Repapis,C.C.,Zerefos,C.S.,Ziomas,J.C.,1992.Assessmentof thepotentialforphotochemicalairpollutioninathensacomparison of emissions and air pollutant levels in Athens with those in Los Angeles.JournalofAppliedMeteorology31, McCollister, G. M., Wilson, K. R., Linear stochastic models for forecasting daily maxima and hourly concentrations of air pollutants. AtmosphericEnvironment(1967)9, Milionis,A.E.,Davies,T.D.,1994.Regressionandstochasticmodelsforair pollution. 1. Review, comments and suggestions. Atmospheric Environment28, Nagendra,S.M.S.,Venugopal,K.,Jones,S.L.,27.Assessmentofairquality near traffic intersections in Bangalore city using air quality index. Transportation Research Part D: Transport and Environment 12, Polydoras, G.N., Anagnostopoulos, J., Bergeles, G.C., Air quality predictions: dispersion model vs BoxJenkins stochastic models. An implementationandcomparisonforathens,greece.appliedthermal Engineering18, Rajeevan,M.,Pai,D.S.,Rohilla,A.K.25.Newstatisticalmodelsforlong range forecasting of southwest monsoon rainfall over India. NCC Research Report, National Climate Centre, India Meteorological Department,Pune 415. Robeson,S.M.,Steyn,D.G.,199.Evaluationandcomparisonofstatistical forecastmodelsfordailymaximumozoneconcentrations.atmospheric EnvironmentPartBUrbanAtmosphere24, Sanchez, M.L., Pascual, D., Ramos, C., Perez, I., 199. Forecasting particulate pollutant concentrations in a city from meteorological variables and regional weather patterns. Atmospheric Environment

9 444 KumarandGoyal AtmosphericPollutionResearch2(211) PartAGeneralTopics24, Sanchez, M.L., Casanova, J.L., Ramos, M. C., Sanchez, J.L., Studying the spatial and temporal distribution of SO 2 in an urban area by principalcomponentfactoranalysis.atmosphericresearch2,5365. Shi,J.P.,Harrison,R.M.,1997.RegressionmodellingofhourlyNO X andno 2 concentrations in urban air in London. Atmospheric Environment 31, Sousa, S.I.V., Martins, F.G., AlvimFerraz, M.C.M., Pereira, M.C., 27. Multiple linear regression and artificial neural networks based on principalcomponentstopredictozoneconcentrations.environmental ModellingandSoftware22,9713. VandenElshout,S.,Leger,K.,Nussio,F.,28.Comparingurbanairquality ineuropeinrealtimeareviewofexistingairqualityindicesandthe proposalofacommonalternative.environmentinternational34, Ziomas, I.C., Melas, D., Zerefos, C.S., Bais, A.F., Paliatsos, A.G., Forecasting peak pollutant levels from meteorological variables. AtmosphericEnvironment29,