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Accounting for traffic speed dynamics when calculatingCOPERT and PHEM pollutant emissions at the urban

scaleDelphine Lejri, Arnaud Can, Nicole Schiper, Ludovic Leclercq

To cite this version:Delphine Lejri, Arnaud Can, Nicole Schiper, Ludovic Leclercq. Accounting for traffic speed dynamicswhen calculating COPERT and PHEM pollutant emissions at the urban scale. Transportation researchpart D: Transport and Environment, 2018, 63, pp.588-603. �10.1016/j.trd.2018.06.023�. �hal-01922400�

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TransportationResearchPartD63(2018)588–603AccountingfortrafficspeeddynamicswhencalculatingCOPERTand

PHEMpollutantemissionsattheurbanscaleDelphineLejri1,ArnaudCan2,NicoleSchiper1,LudovicLeclercq11Univ.Lyon,ENTPE,IFSTTAR,LICIT,F-69518Vaulx-En-Velin,France2IFSTTAR,AME,LAE,F-44344Bouguenais,FranceAbstractCoupling a traffic microsimulation with an emission model is a means of assessing fuelconsumptions and pollutant emissions at the urban scale. Dealing with congested statesrequires the efficient capture of traffic dynamics and their conditioning for the emissionmodel. Two emission models are investigated here: COPERT IV and PHEM v11. Emissioncalculations were performed at road segments over 6 min periods for an area of Pariscovering 3 km2. The resulting network fuel consumption (FC) and nitrogen oxide (NOx)emissionsare thencompared.Thisarticle investigates: (i) the sensitivityofCOPERT to themeanspeeddefinition,and(ii)howCOPERTemissionfunctionscanbeadaptedtocopewithvehicledynamicsrelatedtocongestion. Inaddition,emissionsareevaluatedusingdetailedtrafficoutput(vehicletrajectories)pairedwiththeinstantaneousemissionmodel,PHEM.COPERT emissions are very sensitive to mean speed definition. Using a degraded speeddefinition leads to an underestimation ranging from -13% to -25% for fuel consumptionduring congested periods (from -17% to -36% respectively for NOx emissions). Includingspeed distribution with COPERT leads to higher emissions, especially under congestedconditions (+13% for FC and +16% for NOx). Finally, both these implementations arecompared to the instantaneous modeling chain results. Performance indicators areintroduced to quantify the sensitivity of the coupling to traffic dynamics. Using speeddistributions, performance indicators are more or less doubled compared to traditionalimplementation,butremainlowerthanwhenrelyingontrajectoriespairedwiththePHEMemissionmodel.Highlights

• The mean speed definition has a considerable impact on COPERT FC and NOxemissions,evenatthenetworkscale.

• COPERTfunctionsareadaptedtorichertrafficinformation(speeddistribution).• Modeling chain comparison: traffic microsimulation is paired with PHEM and

COPERT.KeywordsTraffic microsimulation, network emission modeling, mean speed definition, vehiclekinematicsrepresentation,comparisonofCOPERTandPHEM

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1 IntroductionRoad traffic emissions have dramatic local and global effects. Pollutants such asNitrogenOxides (NOx) and Particulate Matter (PM) have known detrimental impacts on humanhealth, including respiratory and cardiovasculardiseases (Shaughnessy et al., 2015),whileCarbon Dioxide (CO2) emissions greatly contribute to global warming. Accurate traffic-relatedemissionestimationsare thuscrucial toassess theirevolutionsover several years,andtoquantifytheenvironmentalimpactofsustainabletransportationpoliciessuchaslow-emission zones and traffic regulation strategies. Emission estimations should be based onmodelsdevelopedforthegivenscaleofinterest,whichcanrangefromverylocal(e.g.,fortheassessmentofcertain road traffic facilities) toglobal investigations (e.g., forcompilinginventories),andthereforerelyonbothrelevantrepresentationsofroadtrafficandvehicleemissions.Adetailedreviewofvehicleemissionmodelscanbefoundin(Smitetal.,2010),while(FallahShorshanietal.,2015)provideareviewofthecompletemodelingchain(traffic,emission,dispersionandstormwater).The main current research efforts focus on the urban scale, because urban road trafficcauses the vehicle kinematics that generate the highest emissions, namely rapid speedvariationsandcongestions,andtheyarethemostdifficult totake intoaccount(Maetal.,2015)(AhnandRakha,2009),(DeVliegeretal.,2000)(Zhangetal.,2011)(Quetal.,2015).Models based on vehicle representations have been developed to overcome theseproblems.Microscopic trafficsimulationprovidesdetailedvehicularkinematics,namelyanestimateofthe1s-evolutionofspeedandaccelerationforeachvehicleonthenetwork.Thusitcancapturecongestioneffectsatthefinestspatialandtemporalresolution.Theestimatedtraffic data are provided for an instantaneous emissionmodel which uses speed profiles(ChenandYu,2007)orderivedindicatorstoestimateemissions(Freyetal.,2010;Jiménez-palacios,1999).Suchmodelinghasbeenadvantageouslyusedforassessingtrafficregulationstrategies such as traffic signal synchronization and speed reduction (Madireddy et al.,2011).However, biases introduced by this coupling have been highlighted, especially concerningsimplifiedvehicletrajectories(VieiradaRochaetal.,2013)andcalibrationprocesses(Jieetal.,2013)(Xuetal.,2016)(Lu,2016).Integratingemissionsintheoptimizationfunctioncanhelptoreducethesebiases(VieiradaRochaetal.,2015).Microscopic emissionmodels entail long computation times, which confine them to localinvestigations. Aggregated models have been developed for broader scale assessments.Thesemodelsrelyonsimplifiedkinematicsvariables,suchasvehiclemeanspeed(SamarasandGeivanidis,2005),whichisthetrafficparameterthatmostinfluencesemissions(Hansenetal.,1995)(Ericsson,2001)(Joumardetal.,2000)(AndréandHammarström,2000)(AndréandRapone,2009).Modelsbasedonmeandrivingspeedsarelesssuccessfulwithcongestedsituations(R.Smit,Brown,&Chan,2008).Indeed,thesemodelsimplicitlytakevaryinglevelsofcongestionintoaccount,dependingontheaveragespeedandtheroadtypechosen(andthedrivingcycleassociated). But they have not been developed to produce accurate local emissionpredictions. Several alternatives have been proposed to overcome this drawback. (RobinSmitetal.,2008)reconstructedaspeeddistributionfromtheavailablemeanspeedonroad

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sections. (Pitsiava-Latinopoulou et al., 2014; Samaras et al., 2014) proposed usingaggregated models at spatial scales smaller than the scale to which they were initiallydedicated,uptotheroadsegmentscale.However,thiscallsintoquestionthetemporalandspatialscalesatwhichthemodelingchoicesmaderemainrelevant.(Samaras et al., 2017) proposed an evaluation for a 1.6 km long urban corridor based onmicro-scale data (models andmeasurements). The authors showed that average speed isstronglycorrelatedwithcongestion.Therefore,theaggregateemissionsmodel(COPERT5)iscongestionsensitiveandmorerelevantfordepictingloadedratherthanfluidsituationsandtheireffectsonEURO5dieselvehiclefuelconsumption.In essence, road sections and short time scales (traditionally 6 min periods, withelectromagneticloopmeasurements)arerelevantforobservingtrafficonanurbannetwork.This scale provides information on vehicle dynamics that characterize congestion throughaggregatetrafficvariablesandraisesquestionsregardingtheemissionmodelthatshouldbeinterfaced with these traffic data at this scale of interest. Therefore, it seems crucial tohighlight emission-modeling representations that are compatible with the outputs of thetrafficmicrosimulation.The key objectives of this article are: (i) to evaluate the impact of traffic informationprocessing on the emissions obtainedwith an aggregatedmodel, and (ii) to compare theemissions over the network obtained with an aggregated emission model and aninstantaneous one. Section 2 presents the simulation framework and the models tested.Section3presentsalternatives tousualaggregatedmodels.Sections4and5comparetheemissionestimationsforacasestudy.Finally,section6concludesonmodelingchoicesforurbanemissionassessment.

2 MaterialCouplingtrafficvariabledefinitionswithemissionmodelsistestedbycomparingestimatedfuel consumptions and NOx emissions over a simulation network. The tested emissionmodels are COPERT and PHEM, which rely on average travel speeds and instantaneousindividualspeeds,respectively.TheversionsofCOPERTandPHEMusedareCOPERTIVandPHEM v11, respectively (see section 2.2). The traffic data required are provided by thedynamic traffic platform Symuvia, which can supply input data from individual vehicletrajectories to aggregated speeds for each vehicle category at given locations on thenetworkandatanytemporalresolution.

2.1 Trafficsimulation2.1.1 TrafficmodelandsimulationThenetworkstudied isa3km2zonecoveringpartof themunicipalitiesofLePerreux-sur-MarneandNeuilly-Plaisance in theParis region.Thetrafficnetwork,displayed inFigure1,was selected for its wide range of traffic conditions. Two structural arterials, “Boulevardd’Alsace-Lorraine”and“ruePasteur”,bothorientedintheeast-westdirection,crossthesiteand feed it with dense traffic. The rest of the site is composed of a fewmain corridors

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(shown in blue in Figure 1), and a large number of residential streets crossed by lightvolumesoftrafficlimitedinspeedto30km/h.Thetrafficmicrosimulationwas implemented intheSymuviaplatform1,whichgivesaccesstotheposition,speedandaccelerationofeachvehicleonthenetworkwitha1s-resolution.Vehicleroutingchoicesaregovernedbyadynamictrafficassignmentmodel,whichguideseachvehicleinthenetworkontheroutethatminimizesitstraveltimetoitsinitiallyassigneddestination. Vehicle movements at themicroscopic scale are governed by a set of rules,includingcar-followingmodeling(Leclercq,2007a,2007b),lane-changes(LavalandLeclercq,2008)andspecificmovementsatintersections(ChevallierandLeclercq,2007).Theplatformalso copes with the cohabitation on the network of vehicles with different kinematics,includingpassengercars,busesandheavy-dutyvehicles.Thequestionofusingtheplatformoutputsforpollutantemissionestimationswasaddressedin(VieiradaRochaetal.,2013).

Figure1.SimulationnetworkimplementedinSymuvia.Left:roadnetworkandOrigin/Destinationtrafficdemands.Right:

Meanweekdaytrafficcountsforpassengercarsandheavydutyvehicles

The simulation consists of 2.5 hours representing the morning rush hour. The Origin-Destination matrix was calibrated with hourly traffic flow rates measured on typicalweekdaysat24locationsofthenetwork(seeFigure1).ThecalibrationresultsaredepictedinFigure2.

1http://www.licit-lyon.eu/themes/realisations/plateformes/symuvia/

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Figure2:measured(red)andestimated(blue)trafficflowrates(veh/h)overtime(hours)at12locations.

2.1.2 Trafficoutputs

ThemostrefinedavailabletrafficoutputsprovidedbySymuviaarethevehiclespeedsandaccelerationsateachtime-step(1s),forallthevehiclesonthenetwork.Thistrafficmodelhas theparticularadvantageofavoiding theunrealisticaccelerations thatcanbe found intraffic microsimulation (Leclercq, 2007b). Indeed, the traffic simulator used – Symuvia –producessimplifiedvehicletrajectories.However,itallowsconformingtorealisticspeedandaccelerationvalues,dependingonthetypeofvehicle.Thus,eachvehicletypeisassociatedwithamaximumaccelerationperspeedrange.Forexample,between20and30km/h,lightvehiclescanacceleratebyamaximumof1m/s2,whileheavyvehiclescannotacceleratebymorethan0.6m/s2.Above30km/h,theselimitsdecreaseby0.5m/s2,0.3m/s2respectively.Figure 3 shows the speed-acceleration pairs experimented during the simulation undercongestedconditionsforlightandheavyvehicles.ThesevehicletrajectoriescanbeuseddirectlytocalculateemissionswithPHEM(includingadefaultgearshiftmodel),oraggregated into trafficvariables inorder tocorrespondto therequiredCOPERTinputs(seesection2.2).Inbothcases,thetrafficoutputswillbeprovidedfor each road segment with a 6min-resolution, andwill be interfaced at that scale withemissionmodels.

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Figure3Speedaccelerationdistributedundercongestedconditionsforlight(left)andheavy(right)vehicles

When a trafficmicrosimulation is available, we can characterize the spatialmean speedsmostrelevant forevaluatingpollutantemissions.However, it isalsopossibletoreproducethecasewheretheleveloftrafficinformationislessaccurateandwheretheaveragespeedsare characterizedbyelectromagnetic loops. In this case,basedonpunctualmean speeds,emissions can be assessed as can the deviations from a more comprehensive trafficdescriptionobservedinthesameconditions.In this paper, various speeddefinitions are compared for qualifying vehicle kinematics oneachroadsegment,thusleadingtoanincreasinglevelofdetail:

1. Theoperational(ordefault)definitionassumesthattheaveragespeedisthespeedlimitVlimit,whichisthefirstoperationalinformationavailable.

2. The speed experimented at one specific location on the road segment Vpunctualcorrespondstothelocalmeasureperformedfor instancebyelectromagnetic loops.Threevirtualpositionsaretested,correspondingtothefollowinglocations:25%,50%and 75% of each segment length, from the beginning of the road segment.Associating the speed on a road segment to Vpunctual amounts to assuming thatvehiclespeedsarehomogeneousalongthesegment.

3. The speed characterizing the vehicle kinematicson thewhole road segmentVspatialcanbedeterminedusingEdie’sdefinition(Edie,1965), inwhichthespatialspeedisthe ratio between the total travel distance and the total spent time. This speeddefinition is themost accurate and compatiblewith the emission estimations, butunfortunatelyitreliesondatanotavailableonarealnetwork.

These three speed definitions can differ significantly, in particular under congestion, asshown inFigure4.Asexpected, thespeed limitVlimitoverestimates theactual speeds.Thewider the vehicle mean speed distribution on the road segment, the larger the errors.Punctual loopsalsoresult inspeedoverestimations,a longacknowledgedbiasdeterminedbythelocationoftheloop.Indeed,attheurbanscale,loopsclosetosignalsaresubjecttomuch more congestion. The impact of these different speed definitions on the resultingemissionerrorsisinvestigatedinsection4.

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2.2 EmissionmodelsThesetrafficvariablesareusedbytheemissionmodelstoestimatefuelconsumptions(FC)andNOxemissions in thenetwork. The two typesofemissionmodel investigatedare themodalmodelPHEMv11andtheaggregatedmodelCOPERT IV.Onlyhotexhaustemissionsareconsidered.Indeed,althoughcold-startandevaporativeemissionscanamounttoanon-negligibleproportionoftotalemissions,itcanbeassumedthatboththepotentiallyinitiatedtrafficstrategiesandthevehiclekinematicsreproducedaffecttheminthesamewayastheyaffecthotexhaustemissions.Vehicle emissions strongly depend on the vehicle’s characteristics, namely the vehiclecategory(passengercars,buses,etc.)and,withineachcategory,fueltype,age,technology,andemission standard (Euro4,Euro5,etc.)of thevehicle.Thevehicle fleet isoneof theparameterssetthroughoutthestudy.ThisfleetistheFrenchurbanfleetfortheyear2015obtained fromthe IFSTTAR fleetupdated in2013.Thispassengercar fleet is composedof30%EURO5dieselvehiclesand24%EURO4dieselvehicles,whereasthelightcommercialvehiclefleetiscomposedof45%EURO5dieselvehiclesand30%EURO4dieselvehicles.Thevehicleclassesaredividedasfollowstofitthetrafficmicrosimulation:82%passengercars,14% light commercial vehicles, 3% heavy duty vehicles and 1% urban buses. Theinterpretationofthiscarfleetbybothmodelingapproachesdiffers,whichcanbeasourceofdiscrepanciesbetweentheemissionsestimated.2.2.1 COPERTIV

COPERTIVhasbeenwidelyusedinmostEuropeanCountriesforcompilingnationalemissioninventories(Ntziachristosetal.,2009),butitisalsoincreasinglyusedforemissionmodelingat the street level (Borge et al., 2012). Concretely, this requires relying on the averagespeedsandtraveldistancesprovidedbyatrafficmodelormeasurementsateachperiod,foreachroadsegmentandvehiclecategory,andthenapplyingtheCOPERTspeedcontinuousfunctionsovereachoftheseroadsegments.However,thisuseatspatialscaleslowerthan

Figure4:Left:extractofthevehicletrajectoriesprovidedbySymuvia.Right:Meanspeedevolutionaccordingtoitsdefinitiononthearterial“Boulevardd’Alsace-Lorraine”.

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thedrivingcyclesissubjecttoquestion.Indeed,theactualroadsegmentspeeddistributionsmight differ from those of the driving cycles, and lose representativeness for very smallsamplesorspecifictrafficconditions(e.g.inthevicinityofintersections),yieldinginaccurateemissionestimates.COPERTreliesonmeandrivingspeedandtraveldistance(totaldistanceinkmtravelledpervehicleforagivenperiod)topredicttherelatedexhaustemissions.Thetotalemissionsarecalculatedastheproductofthetraveldistanceandtheunitaryemissionfactors,accordingto formula (1). Unitary emission factors consist of speed continuous functions that havebeenconstructedoverdrivingcyclesofabout6mn-length,whicharerepresentativeofthetrafficconditionsencountered(AndréandRapone,2009).Theseunitaryemissionfunctionsare defined for each pollutant k and each vehicle class𝑐(e.g. passenger cars, light dutyvehicles,busesandheavydutyvehicles).Theunitaryemissionfunctionofaspecificclassisobtainedbyusingaweightedaverageof thevehicle technologies that compose theclass.Consequently,theemissionsE!,! (g)arecalculatedas:

E!,! = D!. F!,! V! (1)with𝑭!,! beingtheunitaryemissionfactor(g/km)ofpollutantkandvehicleclass c,

𝐷! thetotaltraveldistance(km)and𝑉! themeanspeedforvehicleclass c.Thus,withinavehicleclass,themodelconsidersthesamemeanvehicle(obtainedforafixedcar fleet) whatever the period and the road segment size. The model then omits thedispersion in emissions due to the variability in the actual car fleet observed for smallperiodsandroadsegments,i.e.whenthenumberofobservedvehiclesissmall.2.2.2 PHEMv11PHEM(PassengerCarandHeavyDutyEmissionModel)calculatesthefuelconsumptionandemissionsofvehicleswitha1s-timeresolution,basedontheirlongitudinaldynamicsandonengineemissionmaps(Hausberger,2003;Hausbergeretal.,2003).Themodelfirstprovidesanestimateofthe1s-enginepowerofavehicle,onthebasisofitsspeedtime-seriesandtheroad gradient. The engine speed is estimated using transmission ratios and a gear shiftmodel.Engineemissionmapsthenallowestimatingthetimeevolutionoffuelconsumptionsandairbornepollutantandparticulatematteremissions.Themodelalsoincludestransientcorrectionfunctions,andacoldstarttool.ColdstartemissionswillhoweverbedisregardedtoenablecomparisonwithCOPERT.PHEM is thus appropriate for couplingwithdynamic traffic platforms intended toprovidevehicle trajectories. Such coupling has been performed on several occasions to test theimpact on emissions of road traffic strategies that modify vehicle kinematics behavior(Zallinger,2009).However,theinadequacybetweenthehightrafficdataresolutionrequiredandtheavailabledynamictrafficmodeloutputs,whicharemuchlessrefinedorsubjecttoinaccuracies,canleadtosignificantdiscrepancies(VieiradaRochaetal.,2015).InPHEM,eachindividualvehicleofthesimulationisassociatedwithonespecificvehiclethatcomposes the car fleet,with its ownvehicle technology. Thus, in theory themodel copeswiththesmall-scalevariationsoftheactualcarfleetsobserved;consequently,periodswithsimilarvehiclekinematicsconditionscanresult indifferentemissions.The fitbetweentheactualandthemodeledemissionvariabilityis,however,akeyfactor.

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3 ApplyingCOPERTattheroadsegmentscaleCOPERTemissionfactorsarecontinuousandnon-linearfunctionsofvehicleaveragespeeds.Therefore,theirapplicationattheroadsegmentscaleandwithsmallperiodsfirstrequiresevaluating the sensitivity of the model to mean speed variations. Second, it requiresadaptationstohandlethemeanspeedsbelow10km/hthatarefrequentatsmalltimeandspace scales, and cope with the vehicle trajectories provided by the dynamic trafficsimulation. Adaptations to COPERT emission functions are proposed in this section toovercometheseissueswhereappropriate.

3.1 SensitivityofCOPERTtomeanspeedThis section quantifies the impact of variations in the estimated mean speeds on theemissionfactorsestimatedwithinCOPERT,thankstoformula(1).Meanspeedsarerelativelylow under urban driving conditions, and emission factors are highly variable within thisspeed range (Ntziachristos et al., 2009). If we hypothesize that the travel distance isassociatedwithsmallvariationswhoseeffectscanbeneglected,thentherelativeerrorsonemissionsareonlyduetothebiasonmeanspeedandcanbeexpressedas:

∆!!= !!

!! !!

∆!!

(2)These relative emission errors in terms of speed errors are depicted for FC and NOxemissionsinFigure5.Thefigurehighlightsthelowaccuracyofspeedestimatesneededforactual speeds around 70 km/h, which can be explained by the known low variability ofemissionsinthisspeedrange.Conversely,theneedforaccuratespeedestimatesincreasesatlowspeeds.

Forexample,at30km/h,a2km/herroronthemeanspeedestimateswill leadtoa3.1%errorontheFCestimateanda3.9%errorontheNOxemissionestimate.Atthesametime,a10km/h error will lead to a 15.7% error on the FC estimate and a 19.3% error on NOxemissions.These percentages correspond to errors on themean speed values commonly

Figure5RelativeerrorsonfuelconsumptionandNOxemissionsrelatedtomeanspeedvariationsfrom2to10km/h

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reached throughbothmodeling and in situmeasurements. Thus, at theurban scale, suchlevelsofbiasarenormallyexpected,especiallyatsmalltimeandspatialscales.

3.2 AdaptingtheCOPERTmodel3.2.1 CopingwithlowmeandrivingspeedwithinCOPERTInFigure6, theFCandNOxemissionfactorsF k(ing/km)aredrawn intermsofthemeanspeed.TheCOPERTmodelhandlesonlymeanspeedshigherthan10km/h,althoughmeanspeedsbelow10km/hcanbeencounteredattheroadsegmentscaleforsomeofthe6min-periods. As emissions are definitely not insignificant at that speed range, the COPERTemission curves are extended by either maintaining the EF value at 10 km/h (straightextension), or drawing out the EF curve fitted with a 4th degree polynomial (polynomialextension).Theconsequencesofthesechoicesarediscussedinsection4.

3.2.2 InstantaneousmeandrivingspeedThe dynamic traffic simulation makes it possible to describe the vehicle kinematicsassociatedwitha roadsegmentandaperiod inamoredetailedway thanameandrivingspeed.Thedistributionoftimespentandthedistributionofthetraveldistancesperspeedclass are, for instance, available, possibly refining the emissions calculated with COPERT.However,theCOPERTemissioncurvesarenotdesignedtoacceptsuchfineinputdata.TheCOPERTmodel isadapted inthissectiontomake itcompatiblewithhigh-frequencytrafficdatainputs.Theseadaptationsconsistin:(i)treatingidlingtimeseparately,asitisaspecificpartofthespeedclassdistribution,and(ii)rewritingtheemissionfactorfunctionstorevealthedependencyoninstantaneousspeedsratherthanonspatialmeanspeeds.

Figure6Extendedemissionfunctionsforlowmeanspeed(left:FCfunction;right:NOxfunction)

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Theparticularcaseofidlingtimecanrepresentfrom23%to42%oftimespentonnetwork.The PHEM model provided the values of idling emissions for each pollutant and vehiclecategory.Forinstance,forpassengercars,idlingFCissetat0.17g/swhereasNOxemissionsaresetat0.0011g/s.Whenconsideringanaverage speedasadistributionof instantaneous speedsaround thisaverage, a mathematical formulation of the emission curves as a function of theinstantaneous speeds is determined using a convolution. However, using this newexpression, emissions are always calculated at the scale of a vehicle flow and not at theindividualscale.InaccordancewiththespiritoftheCOPERTmethodology,emissionfactorsare defined for each vehicle category by integrating the fleet distribution within thatcategory. COPERT emissions functions are therefore fitted and transformed into suitablefunctions with instantaneous speeds. We consider that each mean speed V stands for arangeofexperimentalinstantaneousspeeddistributedintheinterval[𝑉 –𝛼; 𝑉 + 𝛼],whichfollows a uniform distribution𝑑!, with𝜎! = 𝛼!/3. Thus, the emission associated with ameanspeedVcanbeseenasamixtureofemission levelsexperimented for thedifferentinstantaneous speed classes. The emission functions𝑭!,! depending onmean speed𝑉arerewrittenasfollows:

𝑭!,! 𝑉 = 𝑮!,! 𝑤 .𝒅! 𝑑𝑤 !!!!!! (3)

This formula helps to define the instantaneous emission functions 𝑮!,! of interest.Consideringthat𝑮!,! canbeadjustedwitha4thdegreepolynomial,thefirstresultisthatthefunctions𝑭!,! maintainthesamepolynomialform.WithG!,! w = p!

!,! w! + p!!,! w! + p!

!,! w! + p!!,! w+ p!

!,!,equation(3)becomes:

𝑭!,! 𝑉 = (𝑝!!,! 𝑤! + 𝑝!

!,! 𝑤! + 𝑝!!,! 𝑤! + 𝑝!

!,! 𝑤 + 𝑝!!,! ).

12𝛼

𝑑𝑤

!!!

!!!

Figure 7 Travel distanceper 2km/h speed classes over the network under freeflow (left) andcongested(right)conditions

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= 12𝛼 𝑝!

!,! 𝑤!

5 + 𝑝!!,!

𝑤!

4 + 𝑝!!,!

𝑤!

3 + 𝑝!!,!

𝑤!

2 + 𝑝!!,!𝑤

!!!

!!!

= 𝑝!

!,! 𝑉! + 𝑝!!,! 𝑉! + (𝑝!

!,! + 6𝜎! 𝑝!!,!) 𝑉! + (𝑝!

!,! + 3𝜎! 𝑝!!,!) 𝑉 + (𝑝!

!,! + 𝜎! 𝑝!!,! +

9 5𝜎!𝑝!

!,!)

Furthermore,considering3rdorderpolynomials,theexpressionoffunctions𝑭!,! isthesamewith a uniform and a normal distribution. With 4th order polynomials, the new curve isformulatedwithbothdistributionsasafourthorderpolynomialbutthecoefficientsdiffer.Inordertoprovideaclearpresentationoftheconcept,hereweexplainonlytheformulationfora4thorderpolynomialandauniformdistribution.The functions𝑭!,! are fitted on existing COPERT curves for each vehicle class c and eachpollutant 𝑘. The fitting process provides numerical values of polynomial coefficients andα. Thelatterisestimatedbetween8and13.Thisisinaccordancewiththespeedstandarddeviationofurbandrivingcycles.The𝑮!,! functions are then derived from the coefficients obtained. These functions,depictedforFCandNOxemissionsinFigure8,resembletheinitialfunctions,butareslightlylowerinthespeedrangeofinterest.

Figure8AdaptedCOPERTemissionfunctions:COPERTemissionfunctionswithstraightextensionfor lowspeed,withthefitted COPERT emission functionspermitting polynomial extension and the emission functions adapted to instantaneousspeed(left:FCestimate;right:NOxestimate)

TheadaptedCOPERTemissionfunctionswillbefurthercoupledtosimulatedtrafficdatainterms of time spent per speed classes. This innovative way of implementing emissionfunctionsisderivedfromequation(1):

𝐸!,! = T!!! .𝑮!,! 𝑉! (4)

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with𝑮!,! the“instantaneous”unitaryemissionfactor(g/s)ofpollutantkandvehicleclass𝑐 𝑇! thetotaltimespentbyvehicleclass𝑐(s)

𝑉! thespeedcharacterizingtheithspeedclass(km/h)

Here,2km/hspeedclasseswereselectedand1svehiclespeedswerereformulatedwiththetotaltimespent ineachspeedclass.Thecorrespondingnetworkemissionsareanalyzedinsection4.2.

4 Sensitivity of COPERT to the speed definitions for emissionscalculatedatthenetworkscale

4.1 SensitivitytospeeddefinitionTheFCandNOxemissionsarecalculatedateachroadsegmentevery6minbyformula(1),and then summed to observe the impact of speed definition on the emissions calculatedoverthenetwork.Thecalculatedemissionsobtainedwiththespatialmeanspeedserveasreferences,asthisspeeddefinitionisthemostaccuratethatcanbeencountered.Figure 9 represents the network emissions for each 6min period, obtainedwith COPERT(straightextensionforthelowestspeeds)andthevariousspeeddefinitions.Degradedspeeddefinitions(speedlimitandpunctualloops)leadgloballytounderestimatedemissions.Thediscrepanciesbetweenthecalculatedemissionsalsodependontheperiod,andreachtheirmaximumvalueduringcongestion(greyarea).Figure96minfuelconsumption(left)andNOxemissions(right)overthenetworkduringthemorningpeakforthevariousspeeddefinitions.

Atthenetworkscale,thepositionsofthevirtual loopsdonothaveasignificant impacton

the estimated emissions. Thus, only virtual loops positioned in the middle of the roadsegment (the 50% loop) are kept in the rest of this article. Using the loop detectors to

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estimatemeanspeedsintroducesdiscrepanciesontheglobalemissionsatthe6minperiodscalethatrangefrom-9.7%to-13.4%forFC,andfrom-13.5%to-17.1%forNOx,comparedwiththeglobalemissionsobtainedwiththespatialmeanspeeddefinition.Usingthespeedlimit to estimatemean speeds introduces anemissionbias at the6minperiod scale thatrangesfrom-19.8%to-25.3%forFC,andfrom-30.7%to-36.0%forNOx.Figure 10(a)

representsthespatialdistributionofthediscrepanciesonemissionscalculatedattheroadsegmentscale foraspecificcongestedperiod,according to thespeeddefinition.The localerrorsarehigherthantheglobalones,especiallyundercongestion.ForNOxemissions,themean relativeerrorusing the speed limit ranges locally from -67.2% to+4.6%,and from -64.5%to73.0%,usingthepunctualmeanspeed.The punctual mean speed definition yields an almost null bias for 47.8% of the roadsegmentsforthisperiod.Indeed,almostathirdoftheseroadsegmentsdonotsignificantlycontribute to the network emissions. This can be explained by the heterogeneity of thenetwork (in terms of geometry and/or traffic). More specifically, Figure 10(b) represents the spatial distribution in terms of percentage of total emissions. Using aspeed limitas themeanspeedforemissionestimation leadstoanearlynull localerror in28% of the road segments, with represents around 3% of the total emissions. On the

Figure10(a)DistributionoflocalrelativeerrorsonNOxforacongestedperiodassociatedwithadegradedspeeddefinition:Speedlimit(left);Punctualmeanspeed(right)–intermsof%ofroadsegments.(b)DistributionoflocalrelativeerrorsonNOxforacongestedperiodassociatedtoadegradeddefinitionofspeed:Speedlimit(left);Punctualmeanspeed(right)–intermsof%ofthetotalemissions

(a)

(b)

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contrary, when it comes to small sets of road segments associated with huge local gaps(around-60%),thesecancontributeto13%ofthetotalemissions.Thespatialanalysisrevealsthatlocallythebiascanbedramaticallyhigher.However,italsoshowsthatthenecessaryaccuracyonmeanspeedcanbeconsideredintermsofemissionstakes and is not homogeneous over the road segments. For further analyses, themeanspeeddefinitionchosenwillbethespatialmeanspeed.

4.2 SensitivitytotheCOPERTadaptations4.2.1 ReferencescenarioTheCOPERTadaptationsproposedinsection3.2arecomparedinthissectionforemissionsbasedonthevehicletrajectoriesprovidedbythedynamictrafficsimulation.Figure11showsthe discrepancies in emissions calculated over the network for the three COPERTadaptationsforfreeflowandcongestedperiods(greyarea).

Figure11COPERTnetworkFC(left)andNOxemissions(right)evaluatedthanksusingthreeadaptedemissionfunctions(seesection3.2).

Considering themean speed approach, using a polynomial extension of COPERT emissionfunctionsimplicitlyresultsinintegratingsurplusemissionsassociatedwithverylowspeeds.This is confirmed at the network level: FC (and NOx emission) is therefore lightlyoverestimated,around1.7%(2.6%forNOx)andatmost3%(4.6%forNOx),comparedwiththestraightextensionofemissionfunctionsthatserveasreferences.Itisinterestingtonotethatthesetwostrategieshavelittleimpactontotalemissions/consumption.On the other hand, using adapted COPERT emission functions introduces a slightunderestimation infreeflowconditionsandanoverestimationcomparedwiththestraightextension of emission curves. This approach, treating traffic information as time spent byinstantaneousspeedclasses,resultsindiscrepanciesatthenetworkscalethatrangefrom-

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1.1%to12.8%forFC(from-1.5%to15.9%forNOxemissions),thatistosay4.8%(5.4%forNOx)forthewholeperiodof2.5hours.4.2.2 IncreaseddemandscenarioA congested scenario is implemented, with a 30% increase in demand, to highlight thediscrepancybetweenthemodelsundercongestion.Intheseconditions,thegapsassociatedwiththeuseofpolynomialextendedCOPERTemissionfunctions(vsstraightextendedEF),are slightly accentuated and reach amaximumof 7% for FC and8.8% forNOxemissions.Thus, the discrepancies betweenmean speed and speed distribution approaches are alsoincreased(from-0.8%to43.2%forFCandfrom-1.3%to45.2%forNOxemission).Thetotalgapfor the whole periodreaches a 15.3% discrepancy for the FC estimate and a15.2%discrepancyforNOxemissions.The gap between the two approaches is revealed in Figure 13 (speed distribution versusmean speed) by comparing the NOx emission contribution of each speed class and both

scenarios.InFigure13.a,the2km/hbinsaredefinedoninstantaneousspeedandintegratedinthecalculationastimespentinthespeedclassconsidered.InFigure13.b,the2km/hbinsaredefinedfora6minmeanspeedandintegratedinthecalculationasdistancetravelledatthe speed class considered. These distributions show the major contribution of emissionassociatedwithidlingtime,whichistreatedindividuallyinthefirstcasebutmixedinthe6min mean fleet speed. This effect is even more significant for the increased demandscenario,where the vehicles under congestion are stopped for 37.6% of the time, versus26.2%forthereferencescenario.

Figure12COPERTnetworkFC(left)andNOxemissions(right)evaluatedusingthreeadaptedemissionfunctionsforthe“increaseddemand”scenario.

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Figure13ContributiontoNOxemissionbyspeedclassesintermsofinstantaneousspeedor6minmeanspeedfora6min-congestedperiod.

TheuseofspeeddistributionsprovidedbythedynamictrafficsimulationleadstohigherFCand NOx emissions, especially during congested periods (grey area). This traffic datatreatmentiscertainlyassociatedwithbetterintegrationoflowspeedsandspeedvariability.Thesetrafficconditionsalsocorrespondtothemostemissiveconditions.Thisspecifictraffic-emissioncouplingseemstoevaluaterealemissionconditionsmorepreciselyatthenetworkscale, although this is not validatedexperimentallyhere. In theabsenceof validation, theemissionlevelscouldbecomparedtoemissionsevaluatedusinganinstantaneousemissionmodelsuchasPHEM.

5 ComparisonofemissionsmodelsThissectionisdevotedtoemissioncalculationsattheroadsegmentscale,usingthePHEMandCOPERTmodels.Thegeneralobjectiveofthispaperistouseatrafficmicrosimulationtoevaluate pollutant emissions and to analyze the differences found between theimplementationofdifferentmethodologies.ThehypothesistestedisthattheaggregateCOPERTmodel,basedonaveragespeed,isnotcapable of integrating all the speed variability,which is higher during congestion. On thecontrary,we assume that the PHEMmodel,which relies on vehicle kinematics, is able tointegrate these typical phenomena. Thedifferencesobserved are therefore interpreted inrelationtotrafficdynamics,althoughtheabsolutedifferencesbetweenthemodelsmaybeduetootherorigins.This iswhytheanalysiswillnotconcludeonthebestperformanceofone model compared to another, but rather aim to assess their sensitivity to trafficdynamics.

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5.1 PHEMemissionsAsthemicrosimulationprovidesverydetailedinformationforeachvehicle(1strajectories),the temptation is great to use an emission model able to maintain this level of detail.Despitethehugeamountofdatatobeimplemented(associatedwithapproximately2hourscalculation for one run), the traffic data is compatible with the input data of the PHEMmodalemissionsmodel.

Figure14DynamicnetworkPHEMemissionsresultingfrom15replications.

Figure14representsthetimeevolutionofthefuelconsumption(andNOxemissions)overthe network obtainedwith PHEM.With no information on vehicle technology except forvehicleclasses,themodelstochasticallyassociatesatechnologywithaparticularvehicleofthe class considered (Passenger cars, Light Duty Vehicles, Buses or Heavy Duty Vehicle),conformingtotheinputfleetcompositiondescribedinsection2.2.TheboxplotshowninthefigureisassociatedwithPHEMemissionvaluesover15replications.Thefirstobservationisthat the stochastic fleet definition not only impacts local emissions but also networkemissions. The global relative gaps over time periods range from -5.0% to 3.7% for fuelconsumption,andfrom-8.0%to9.2%forNOxemissions.For the following analysis, the emission evaluatedwith PHEMwill be represented as themeanvalueofthereplicationsforeach6mintimeperiod.

5.2 PHEMandCOPERTemissionsFinally, three modeling chains, starting from the same traffic microsimulation, werecomparedatthenetworkscaleintermsoffuelconsumptionandNOxemissions.Individualtraffic trajectories were coupled with PHEM, whereas COPERT was implemented with

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aggregatedtrafficvariables(spatialmeanspeed)andspeeddistribution(seesection3.2).Alltheenvironmentalassessmentswereproducedforagivenfleettranscribedintheemissionsmodels.Atthedrivingcyclescale,PHEMoverestimatesoverallconsumptioncomparedtoCOPERTincongestedconditions,but the trend is lessmarked forNOxemissions. The issueofmodelconsistencyencounteredbyemissionmodelers isnotaddressedinthispaper.Theauthorsdeliberatelychosenottoartificiallymodifytheparametersoftheemissionmodelstomakethemconsistent.Theanalysisbelowdoesnotfocusonthenominalvaluesproposedbythetools but on their evolution according to traffic conditions. To do this, the emissionsnormalizedby theaveragevalueover theperiodwereplotted forboth scenarioswithoutinvolvingtheinherentdifferencesduetothemodelversionsinuse(seeFigures16&18).

Figure15ComparisonofnetworkFC(left)andNOxemissions(right)withthreemodelingchainsforthereferencescenario

As shown in Figure 15, the PHEMmodal emission model obtains higher emission levels,especially for congestion periods. The gap between COPERT emissions (with spatialmeanspeed) compared to PHEM emissions is quantified: the relative deviations reach-34.6% for fuel consumption (-24.2% for NOx emissions). Using the adapted COPERTemission functions reduced the maximum relative discrepancies to -30.1% for fuelconsumption(-16.5%forNOxemissions).Thismeansthattheresultishighlydependentonthemodelingchain.However,toovercomeversion-relateddeviations,theemissionvalueswerecomparedbymodelbetween fluidandcongestedperiods for the twoscenariosandbetweenbothscenarios(seeTable1).

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Figure 16 Comparison of normalized network FC (left) and NOx emissions (right) with three modeling chainsforthereferencescenario.

Figure 1 shows that all the models follow the overall traffic pattern over the periodconsidered.However,itrevealsthatinafree-flowingsituation,theaverage-speedapproachtends to overestimate NOx emissions/consumption, whereas in congested conditions, ittendstounderestimatethembecauseitdoesnotincludetheeffectsofcongestion.

Thesedifferenceshavebeenquantifiedcomparingtheemissionon(Eon)andoff(Eoff)peakforbothscenariosanddrawingthecomparisonbetweenscenario1and2,distinguishedbythecongestionrate:

δ = 𝐸!" − 𝐸!"" 𝐸!"!#$ x 100

Δ = 𝐸!"!! − 𝐸!"!! 𝐸!"!! + 𝐸!"!! x 100

Theseindicatorsshouldbereadasfollows:thehigherthevalue,themorethemethodologyintegratesthetrafficdynamics.

Table1Performanceindicators(%)reflectingtheintegrationoftrafficdynamics.

NOx PHEM COPERT – speed classes

COPERT – mean speed

δ1 13.8 10.8 6.7 δ2 21.0 15.5 6.3 Δ 13.9 9.9 5.6

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FC PHEM COPERT – speed classes

COPERT – mean speed

δ1 10.7 10.6 7.3 δ2 17.0 17.0 8.0 Δ 13.1 11.8 7.2

The same conclusionwith enhanced effects can be observedwith the increased demandscenarioFigure17and18).ComparingCOPERTtoPHEMemissions, therelativedeviationsreach -46.8% for fuel consumption (-41.5% for NOx emissions). Using adapted COPERTemission functions reduces the maximum relative discrepancies to -32.1% for fuelconsumption(-24.4%forNOxemissions).

Onceagain,thiscomparisonsaysnothingaboutthemorerealisticemissionlevelandthese

results cannot be seen as a recommendation for using one modeling chain rather thananother.Thepurposeistoexhibitthepotentialdeviationsinducedbydifferenttreatmentsofthesametrafficmicrosimulation.

Figure17Comparisonof networkFC (left) andNOxemissions (right)withthreemodeling chains for theincreaseddemandscenario.

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Figure 18 Comparison of normalized network FC (left) and NOx emissions (right) with three modeling chains for theincreaseddemandscenario.

6 DiscussionInacontextwheretransportationmanagersareurgedtotaketheenvironmentalimpactofroadtrafficintoaccount,thechallengeistoprovideanaccuratedynamicalestimationofthenetworkemissions. Indeed, toqualify theexisting situationor traffic regulationmeasures,officials are interested in accurate environmental evaluations. To do this, evaluationmethods,evenatthecityscale,cannotignoretrafficdynamics,thatistosaythecongestionphenomenon.This pointwas stressed in particular in this article: trafficmicrosimulation provides a finerepresentation of vehicle kinematics, which is relevant for emission calculations. Indeed,when comparing emission calculations, each discrepancy observed, even at the networkscale,dependedontrafficconditionsandwasconsiderablygreaterduringcongestion.When implementing emission calculations from vehicle trajectories, an instantaneousmodel,suchasPHEM,seemstobemoreefficient.Thestrategyisdefinitelytime-consumingbut still affordable in terms of the amount of data processed. Nevertheless, this articlespecifiedtheimprecisionduetothefactthatwedonotknowtherealfleetcomposition:thiscaninduceanon-negligibledeviation,evenatthenetworkscale.Withthesimulatedtrafficdata, theabsoluteglobal relativeerror can reach5.0% for fuel consumptionand9.2% forNOxemissions.Regardingaggregatingemissionmodels,suchasCOPERT,thefirststepistodefinetheusefulaggregated traffic variables. This article specifically underlined the need for cautionregarding themean speed definition. The gap associated with a degraded definition wasquantified.Inthecaseofmissinginformation,theroadsegmentlimitspeedcanoccasionallybeusedtoevaluateemissions,leadingtoacriticalbias(-25%forFC,-30%forNOx).

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Finally,anotherapproachwasproposed,improvingtrafficrepresentation:trafficconditionswerenolongersynthesizedwithameanspeedbutwithaspeeddistribution.AtheoreticalreflectionwasproposedtoadapttheCOPERTemissionfunctionstothis inputinformation.Consequently, the evaluation led to a higher emission value. The performance indicatorsweremoreor lessdoubledcompared toa classical implementationand revealed that theintegrationoftrafficdynamicswassuccessful.Thismodelingchainappearedefficientattheurbanscaleincongestedconditions.This article focused on comparing emissionmodels but cannot conclude on favoring onemodelingchainoveranother. Itscontribution lies in thedescriptionof therequisite trafficdynamics: congested periods should be characterized carefully. However, the issue ofvalidation remains to be addressed. It would be interesting to compare these results tomeasurements, such as ambient concentrations, to obtain an idea of the range of realemissionsoverthenetwork.AcknowledgmentsThisworkwasperformedintheframeworkoftheTrafipolluresearchprojectfundedbytheNationalResearchAgencyundercontractno.ANR-12-VBDU-0002-01.ReferencesAhn, K., Rakha, H., 2009. A field evaluation case study of the environmental and energy

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