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A semi-empirical, receptor-oriented Lagrangian model for simulating fine particulate carbon at rural sites

A semi-empirical, receptor-oriented Lagrangian model for simulating fine particulate carbon at rural sites
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  A semi-empirical, receptor-oriented Lagrangian model for simulating  fi neparticulate carbon at rural sites B.A. Schichtel a , * , M.A. Rodriguez b , M.G. Barna a , K.A. Gebhart a , M.L. Pitchford c , W.C. Malm b a National Park Service, CIRA/CSU, 1375 Campus Delivery, Fort Collins, CO 80523, USA b Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, CO 80523, USA c Division of Atmospheric Sciences, Desert Research Institute, Reno, NV 89512, USA h i g h l i g h t s < We present a new semi-empirical Lagrangian particle dispersion model. < The model is used to apportion PM 2.5  carbon at rural locations to major source types. < The results are evaluated against measured data and compared to CMAQ model results. < The model is best used in the analysis of measured carbonaceous aerosols. a r t i c l e i n f o  Article history: Received 24 October 2011Received in revised form9 April 2012Accepted 6 July 2012 Keywords: Lagrangian particle dispersion modelCarbonaceous aerosolsSource apportionmentBiomass burning a b s t r a c t Total  fi ne particulate carbon (TC) is an important contributor to  fi ne particulate matter and is measuredin routine national monitoring programs. TC contributes to adverse health effects, regional haze, andclimate effects. To resolve these adverse effects, there is a need for tools capable of routine and clima-tological assessments and exploration of the sources contributing to the measured TC. To address thisneed, a receptor-oriented, Lagrangian particle dispersion model was developed to simulate TC in ruralareas, using readily available meteorological and emission inputs. This model was based on the CAPITA(Center for Air Pollution Impact and Trend Analysis) Monte Carlo model (CMC) and simulated thecontributions from eight source categories, including biomass burning and secondary organic carbon(SOC) from vegetation. TC removal and formation mechanisms are simulated using a simpli fi edparameterization of atmospheric processes based on pseudo- fi rst-order rate equations. The rate coef  fi -cients are empirical functions of meteorological parameters derived from measured, modeled, andliterature data. These functions were optimized such that the simulated TC concentrations reproduce theaverage spatial and seasonal patterns in measured 2008 U.S. TC concentrations, as well as measured SOCfractions at two eastern U.S. sites. The optimized model was used to simulate 2006 e 2008 rural TC thatwas evaluated against measured TC. In addition, the model output was compared to TC from a 2006Eulerian Community Multiscale Air Quality (CMAQ) simulation. It is shown that the CMC model hassimilar performance metrics as the CMAQ model.Published by Elsevier Ltd. 1. Introduction Carbonaceous aerosols arise from a wide variety of sources,includingcombustionof fossilfuels,meatcooking,deep frying,andbiomass burning (Bond et al., 2004). Secondary organic carbon(SOC) produced from biogenic and combustion volatile organiccompounds (VOCs) also contribute to organic aerosols. The diversecarbon sources and atmospheric processing result in a complexmixture of compounds that signi fi cantly contribute to  fi ne partic-ulate matter (PM)  <  2.5  m m (PM 2.5 ) (Hand et al., 2012). High PM 2.5 carbon concentrations can lead to adverse health effects, theiref  fi cient scattering and absorption of visible and infrared radiationmake them a key factor in the balance of solar radiation, and theycontributetohazeinprotectednationalparksandwildernessareas,i.e., class I areas.The Interagency Monitoring of Protected Visual Environments(IMPROVE) and Chemical Speciation Network (CSN) routinemonitoring networks collect 24-h, integrated PM 2.5  samples thatare analyzed for chemical composition, including organic (OC) andelemental (EC) carbon. The IMPROVE monitoring program is used *  Corresponding author. Tel.:  þ 1 970 491 8581; fax:  þ 1 970 491 8598. E-mail address: (B.A. Schichtel). Contents lists available at SciVerse ScienceDirect Atmospheric Environment journal homepage: 1352-2310/$  e  see front matter Published by Elsevier Ltd. Atmospheric Environment 61 (2012) 361 e 370  to track long-term trends in visibility and haze in protected visualenvironments,consistentwiththeneedsof theRegionalHazeRule.Data are also used to identify chemical species and emissionsources responsible for the haze. The objectives of the CSN are totrack progress of emission control programs, develop emissioncontrol strategies, and characterize spatial and temporal trends inspeciated PM 2.5 .To achieve the goals of these monitoring programs, there isa need for tools capable of routine and climatological assessmentsand exploration of the causes of the measured carbonaceous andother aerosol concentrations. Available tools range from simplebacktrajectorymodelstosophisticatedEulerianchemicaltransportmodels (CTM). Back trajectory/dispersion models are ef  fi cientmodelscapableofsimulatingmultipleyearsofairmasstransporttoone or more receptors, using readily available meteorological data.Trajectoryanalysismethodsgenerallydonotincorporateemissionsor simulate atmospheric removal/formation processes and usesome variation of the residence time analysis method (Ashbaugh,1983). They qualitatively identify transport pathways and broadregions where sources are likely to contribute to the measuredreceptor concentrations. Due to their simplicity and value, trajec-tory analysis methods have seen widespread use in a variety of analyses (e.g., Stohl,1998).Eulerian CTMs are capable of quantitative assessments of thecontributions of source regions and types contributing to thereceptor concentrations. However, CTMs are generally resourceintensive, requiring a variety of data inputs and computer andpersonnel resources. Consequently, source apportionment is typi-cally performed in short-term studies by dedicated modelinggroups, limiting the applicability of these important tools.Inthisworkwestrovetodevelopaquantitativedataassessmenttool more akin to trajectory analyses than Eulerian CTMs that iscapableofapportioningcarbonaceousaerosolmeasuredatremote-area monitoring sites to contributing source types, includingbiomass burning, mobile, and vegetation. A primary goal was thatthe model be readily applicable to short- and long-term dataanalysis studies, requiring the same meteorological inputs as usedin trajectory models, with the only additional data input beingemission  fi elds.To accomplish this, the receptor-oriented (backward time)Lagrangian particle dispersion model (LPDM) (Uliasz and Pielke,1992) approach was used. Receptor-oriented LPDMs model thereceptor concentration as an ensemble of particles that aredispersed back in time. These models readily lend themselves toef  fi cient source apportionment analyses, since they directly simu-late the source e receptor relationship by maintaining a separationbetween sources. In addition, only sources upwind of the moni-toring sites are simulated, making this approach advantageous forinvestigating monitoring data where there are a limited number of receptor sites (Seibert and Frank, 2004). To simulate atmospheric physical and chemical removal and formation processes, a simpli- fi ed parameterization based on pseudo- fi rst-order rate equationswas developed. The rate coef  fi cients are functions of meteorolog-ical parameters and are optimized through a tuning process to  fi tmeasured data. Others have used and proposed LPDMs for quan-titative simulation and assessments of receptor concentrations(e.g., Seibert and Frank, 2004); however, all receptor LPDMs of  which we are aware have employed linear loss and gain mecha-nisms and have not simulated the formation of secondarypollutants.The model was developed and optimized using the IMPROVEtotal  fi ne particulate carbon (TC), i.e., the sum of the measured OCand EC, at rural monitoring sites during 2008, as well as measuredSOC fractions at two eastern U.S. sites. It was then used to simulatethe 2006 e 2007 IMPROVE TC concentrations. Following isa description of the model formulation, the optimization process,and the evaluation of simulated concentrations from 2006 e 2008IMPROVEdata.Inaddition,intheSupplementarymaterialthe2006model simulation is compared to the results from the CommunityMultiscale Air Quality Modeling System (CMAQ) Eulerian CTM. Afollowing paper will examine the source contribution results fromthe 3-year model simulation. 2. Receptor-oriented particulate carbon chemical transportmodeling  Conceptually, the receptor-oriented chemical LPDM works byassuming that the concentration or mixing ratio of a trace speciescan be represented by the averagefrom an ensemble of particles orairparcelsatthereceptorlocationandtime.Theseparticlesare fi rstdispersed for a  fi xed period back in time, with each particlefollowing a unique back trajectory due to random atmosphericturbulence. At the end of the particles ’  trajectories, they are givenan initial concentration and then transported forward in time,following their trajectory pathways back to the receptor. Duringthis forward transport, mass balance is maintained at the particlelevel by modifying its initial concentration by emissions accumu-lated along the trajectory pathway and physical/chemicalprocesses, including deposition and chemical transformations.For the simulation of   fi ne particulate carbon, this methodrequires four components:  fi rst, a backward LPDM and meteoro-logical input data to simulate the history of the receptor airmass;second, an emission inventory accounting for emissions fromvarious source types of particulate carbon andVOCs; third,a modelformulation relating the emissions from sources traversed by thetrajectories to the receptor concentration and the changes in theseemissions due to atmospheric physical and chemical processesduring transport. In this application, the last component entailsparameterization of physical and chemical processes and theiroptimization to  fi t measured data.  2.1. CAPITA Monte Carlo LPDM  The calculation of the receptor airmass histories for the simu-lation of particulate carbon at IMPROVE monitoring sites wasconducted using the CAPITA (Center for Air Pollution Impact andTrend Analysis) Monte Carlo (CMC) LPDM. The formulation of theCMC LPDM model and its use for forward and backward dispersionsimulations has been described elsewhere (Schichtel and Husar,1997; Schichtel et al., 2005a). The CMC model is capable of simulating forward and backwarddispersion, using different meteorological  fi elds and from one tothousandsofparticletrajectories.Inthiswork,theNationalCentersfor Environmental Prediction (NCEP) Eta Data Assimilation System(EDAS) (Black, 1994) meteorological data were used. The EDAS meteorological  fi elds are archived at the National Oceanic andAtmosphericAdministration(NOAA)AirResourceLaboratory(ARL)using a 40-km grid and 26 pressure surfaces every 3 h.Many of the IMPROVE monitors are located in complex terrain.The Lagrangian model and coarse meteorological data are notsuited for simulating potentially important mesoscale features,including channeling by terrain and convective precipitation.However, they are suitable for simulating regional-scale features,and it is assumed that it is regional-scale emissions and meteo-rology that are causing most of the variance in the measuredconcentrations. As will be shown, the model performancedecreases in urban areas and when local  fi res are present. Thisdecreased performance may partly be due to the dif  fi culty of simulating the transport at the smaller scales. B.A. Schichtel et al. / Atmospheric Environment 61 (2012) 361 e  370 362   2.2. Particulate and VOC emission  fi elds A detailed 2002 emission inventory for input into Eulerianchemical transport models using the CBM-IV chemical mechanismwas developed for the Western Regional Air Partnership (WRAP)and used to simulate the impact of PM and haze on national parksand wilderness areas in support of Regional Haze Rule StateImplementation Plans (Brewer and Moore, 2009). This emissioninventory had hourly emission rates from 22 area, point, mobile,and biogenic source categories for 21 different species, includingOC and EC and eight groups of reactive VOC compounds. The areasources were on a 36-km modeling domain covering mostof NorthAmerica and a nested 12-km grid covering most of the westernUnited States.The 36-km WRAP emissions were used for input into the CMCmodel. The emissions from the point sources were summed withthe area source in the grid cell into which each point source fell. Inaddition, the hourly emission rates were averaged up to 24-hvalues, and the 22 source categories were grouped into six cate-goriesasde fi nedinTable1.TheeightVOCemissioncategorieswereaggregated into three categories consisting of a high carbonnumber and SOA yield group (Zhang et al., 2007), a low carbon number and SOA yield group, and isoprene (Table 2). Isoprene wasseparatedfromtheothercompoundsbecauseithaslowSOAyields,but its high emissions result in signi fi cant contributions to SOA(Kleindienst et al., 2007; Carlton et al., 2009). The units of the VOC emission rates were converted to kg C m  2 day  1 using the carbonnumbersinTable2.Theseaggregated2002emissionswereusedforsimulating particulate carbon in all modeled years.Biomass burning is a signi fi cant source of TC, and the emissionlocations, release times, and rates have large variations from oneyear to another. The WRAP biomass burning emissions werereplaced by the National Center for Atmospheric Research (NCAR)regional fi reemissionsmodelversion2.0(Wiedinmyeretal.,2006).This is a North American inventory that estimates the daily  fi reemissions of OC, EC, total VOC, and other species from individual fi res. The location and timing of the  fi res were determined byobservations from the Moderate Resolution Imaging Spectroradi-ometer (MODIS) instruments aboard the Terra and Aqua satellites,and each  fi re encompassed an area burned up to 1 km 2 .The individual  fi res in the emission inventory were gridded tothe same 36-km grid used for the WRAP inventory by aggregatingall  fi res that fell into the same grid cell. There is evidence that  fi reemission inventories overestimate the primary carbon emissionsand underestimate the semivolatile OC and subsequent formationof SOC (Hennigan et al., 2011). This was also seen in initial model simulations in which receptors near  fi res typically overestimatedthe TC. To account for this, the primary emissions were evenlydistributed over 8 h from the release of the  fi re ’ s emissions. Thetracking of the primary TC and formation of this pseudo-SOC wasdone along each particle ’ s trajectory. Based upon land-use data inthe NCAR   fi re emission inventory, the  fi res were classi fi ed as eitheragricultural or other  fi res.  2.3. Chemical transport LPDM formulation There are various formulations of the receptor-oriented LPDM.In this work we follow that set forth by Seibert and Frank (2004),which was based on mixing ratiosandincorporated fi rst-orderrateprocesses. In the Lagrangian framework, they showed that themixingratio c attime t  andlocation r  * foraspeciesaffectedby fi rst-order processes that can vary in space and time for a single parti-cle ’ s trajectory is c  r  * ; t    ¼  c o  p  0  þ Z  t t   s _ q ½ r  ð t  0 Þ ; t  0  r ½ r  ð t  0 Þ ; t  0   p ð t  0 Þ d t  0 (1) where s  is the length of the particle back trajectory in time, units [s] c o  is the particle ’ s initial mixing ratio at time  t     s . _ q  is the source emission rate, units [g m  3 s  1 ] r  is air density, units [g m  3 ]  p ð t  0 Þ isthetransmissionfunction,i.e.,thelossorgaininmassdueto  fi rst-order rate processes during transport from the source tothe receptor along the trajectory during time period  t  e t  0 .Space and time can be discretized such that space is griddedwith index  i ; time at the receptor has index  j ; and time along eachtrajectoryhas N  equaltimestepswithindex n .Itcanthenbeshownthat Eq. (1) becomes c  j z c o  p ð 0 Þ þ X i X  jn ¼  j  N   _ q in r in D t  0 in  p in   (2) where D t  0 in  is the residence time of the particle in grid  i  during the timestep  n p in isthelossorgaininmassfromtimeoftheemissionsningridcell  i  to impacting the receptor at time  j .Theaveragemixingratioatthereceptoroveratimeperiod  J  andthe ensemble of particles  M   at each time step  j  is then c  ¼  1  J  * M  X  j 0 þ  J  j ¼  j 0 X M m ¼ 0 c  jm  (3) The average source contribution can be calculated by  Table 1 Emission categories used in the CMC model.Source category EmissioninventoryDescriptionArea WRAP Stationary area sources, e.g.,residential heating andarchitectural coatingsPoint WRAP Point sources, e.g., electricalgenerating units and oil re fi neriesMobile WRAP On- and off-road mobile sourcesBiogenic WRAP Vegetation gaseous emissionsOil and gas WRAP Oil and gas in the westernUnited StatesOther WRAP Off shore sources, e.g., shipping,and road, fugitive, andwindblown dustAgricultural  fi res NCAR Agricultural  fi resOther  fi res NCAR Wild and prescribed  fi res  Table 2 VOC categories from the CBM-IV chemical mechanism and their correspondingcarbon numbers, combined into high and low reactive VOC categories.VOC category Carbon #High reactive VOC Toluene and other monoalkyl aromatics 7Xylene and other polyalkyl aromatics 8Terpenes 10Low reactive VOC Formaldehyde 1Higher aldehyde 2Ethene 2Paraf  fi n carbon bond (C e C) 1Ole fi n carbon bond (C ] C) 2Isoprene Isoprene 5 B.A. Schichtel et al. / Atmospheric Environment 61 (2012) 361 e  370  363  G  ji  ¼  1  J  * M  X  j 0 þ  J  j ¼  j 0 X M m ¼ 0 X  jn ¼  j  N   _ q in r in D t  0 in  p in   (4) InEq.(4), i representsasourceregion;however,inapplicationitcould also be an individual source or source type.  2.3.1. Particulate carbon physical/chemistry model The backward LPDM formulated in Eqs. (2) and (3) can accom-modate any  fi rst-order process  P(t)  that describes the change inconcentrations due to physical/chemical processes over a giventime period. In this work we are interested in simulating TC. TC isamixtureofprimaryOCandECandSOCcompoundsformedbytheoxidation and condensation of VOCs. The particulate and gaseousspecies can be removed from the atmosphere by dry and wetdeposition. These processes can be modeled using the coupled setsof rate equations: d ð VOC i Þ d t   ¼   k t i  þ  k dg i þ  k wg i  VOC i  (5)d ð TC Þ d t   ¼ X i k t i ð VOC i Þ !   k dp  þ  k wp  TC (6) whereTC is the particulate carbon mixing ratioVOC i  is an individual or class of VOC mixing ratio k t i ,  k dg i , and  k wg i are VOC gas to particulate carbon transformation,dry deposition, and wet deposition rate coef  fi cients,respectively k dp  and  k wp  are particulate carbon dry and wet deposition ratecoef  fi cients, respectively.Although the rate equations are linear, the species-speci fi ctransformation rate coef  fi cients and dry and wet deposition ratescan be nonlinear functions dependent upon the chemical, meteo-rological, and geological environment of the species. Physicalformulations can be developed to model these processes. However,theseformulationstypicallyrequireextensiveinformationanddatathat are often unavailable or dif  fi cult to obtain, requiring a numberof assumptions that can lead to large uncertainties. An alternativeapproach is to develop empirical relationships between the coef- fi cients and readily available meteorological, chemical, andgeophysicalvariableswheretherelationshipsareoptimized sothatthe simulated concentrations are a best  fi t to measured values(SchichtelandHusar,1997).Theempiricalapproachwasused,sincethe intent of this work was to develop a model that capturesimportant spatial and temporal variability but has modest datarequirements and can be routinely operated.  2.4. Empirical rate coef   fi cient equations Dry deposition is a  fl ux of material to the surface and is oftenmodeled as the product of a deposition velocity  v d  and the speciesconcentration. Thedrydepositioncoef  fi cient, k d , foragiven speciesis then k d ¼  v d H ;  (7) whereH is the layer near the surface where dry deposition occurs.Thedrydepositionvelocityofparticulates ð v pd Þ andgases ð v gd Þ aredetermined by atmospheric mixing, which delivers material to thesurface, and by the absorptive properties of the surface. Both of these processes vary spatially, diurnally, and seasonally, in fl uencedbythe solar insulation. Consequently, relationships between v d  andsolar insulation were sought.To explore this relationship,  v pd  from the Clean Air Status andTrends Network (CASTNET) dry deposition monitoring programand VOC  v gd  from a Comprehensive Air quality Model with exten-sions (CAMx) simulation over most of North America werecompared to the surface downward shortwave radiation  fl ux (SR)[kW m  2 ] from the EDAS meteorological  fi elds. In the CASTNETmonitoring program, hourly  v pd  are calculated for each monitoringsite, using the Multilayer Deposition Velocity Model (MLM)(Meyers et al.,1998). The CAMx data were from a 2009 simulationsimilar to Rodriguez et al. (2011).Fig.1 compares the average diurnal cycle of the  v pd  against SR forthe months of January, April, July, and October. The CASTNET  v pd diurnal cycle was calculated by averaging  v pd  over all CASTNET sitesfrom 2000 through 2005 for each hour of the day. As shown, theseaverage  v pd  and SR values are highly correlated, with  r  2 ¼  0.98, andall months have a similar linear relationship.Fig. 2 compares the average diurnal cycle of a VOC-concentration-weighted average  v gd  to SR. The hourly compositeVOC  v gd  were calculated from the CAMx model results at eachIMPROVE site. The average  v gd  for most VOCs varied between 0.03and 0.4 cm s  1 , though some short-lived-reaction products hadaverage  v gd  >  2 cm s  1 . As shown in Fig. 2, the aggregated  v gd  diurnalcycle is highly correlated with SR and has a quadratic relationshipthat varies by season, with higher  v gd  during July than January. The v gd  values during April and Octoberaresimilarand arebetween Julyand January.There are physical explanations for the  v d  relationships with SR.In the MLM,  v pd  is highly dependent upon the aerodynamic layerresistances, and this resistance is dependent on atmosphericturbulence(Vongetal.,2010).Itappearsthat SRisagoodsurrogatefor this turbulence and on average  v pd  is approximately linearlydependent on SR. Dry deposition of gases is also dependent on thecanopy resistance, and as modeled in CAMx, the canopy resistanceis inversely dependent on SR  2 (ENVIRON, 2010).Based on these results,  v pd  and  v gd  were parameterized as linearandquadraticfunctionsofSR,respectively.Thesefunctionsaccountfor the average diurnal and seasonal variation in  v d  but do notaccount for the day to day variation in other important Fig.1.  Scatter plots showing the relationship between the average diurnal cycle in theparticle dry deposition velocity from the CASTNET program and solar radiation for January, April, July, and October. B.A. Schichtel et al. / Atmospheric Environment 61 (2012) 361 e  370 364  meteorological parameters and changing land surface types. Thesein fl uences are signi fi cant, and the coef  fi cients of variation fora given season and hour of the day for both  v pd  and  v gd  were on theorder of one.Wet deposition can be parameterized by introducing a dimen-sionless washout ratio W, which is the ratio of the concentration of thespeciesintheprecipitationtoitsconcentrationintheair.Thewetremoval rate or scavenging coef  fi cient for a given species is then k w ¼  W H  w P  ;  (8) where H  w isawashoutdepth(m)and P  istheprecipitationrate(ms  1 )(Barrie,1981; Andronache, 2004). TC washout ratios vary depending on precipitation types andparticulate properties, including size and hygroscopicity, and canvary by several orders of magnitude, though typical values rangefrom 10 5 to 10 6 (Bidleman, 1988). It is commonly assumed thata slightly soluble trace species in the atmosphere is in equilibriumwith a falling raindrop. Under this condition of equilibrium gasscavenging,asdiscussedbyHartetal.(1993),thewashoutratiocan be estimated as W  g  ¼  RT k H ;  (9) where R  (m 3 atm (K mol)  1 ) is the universal gas constant T   (K) is the temperature k H  (M atm  1 ) is the species effective Henry Law constant. k H  for different VOC species varies over several orders of magnitude. Using the VOC concentrations from the 2009 CAMxmodel simulation at each IMPROVE site and the  k H  for each VOCspecies at 298 K (ENVIRON, 2010), a concentration-weightedcomposite VOC  k H  for the January, April, July, and Octobermonths was calculated that varied from 10 3 to 2    10 3 M atm  1 .These  k H  correspond to  W  g  from 2.3    10 4 to 5.2    10 4 .These TC and VOC washout ratios are large and under moderateto heavy precipitation will ef  fi ciently remove most carbonaceousspecies from the atmosphere. Therefore, only constant averagewashout ratios were used in the model.SOA formation in the atmosphere is dependent on a number of factors, and not all relevant processes are well understood, leadingto broad ranges and high uncertainties in modeled formation ratesand making this an active area of research (Carlton et al., 2009;Hallquist et al., 2009; Hennigan et al., 2011). Most SOC formation is driven by photochemical processes and is dependent on SR. Non-photochemically driven reactions may also be important; forexample, Ng et al. (2008) showed that the SOC formation couldoccur from nighttime reactions of isoprene with nitrate radicals.Evidence also exists for signi fi cant aqueous-phase SOA formation(Hallquist et al., 2009).Given these complications and unknowns, the transformationrate for the high-yield VOCs was made a linear function of SR. Thetransformation rate for the low-yield VOCs and isoprene was set toa constant fraction of the high-yield VOCs. In order to account foraqueous-phase SOA, these transformation rates were increased by50% during precipitation periods.  2.5. Implementation and optimization of the CMC model for TC simulation The CMC model was used to simulate the receptor airmassdispersion at 162 IMPROVE monitoring sites, of which 148 werelocated in remote settings and 14 in suburban/urban settings. Ateach site, 25 particles were released every 2 h and tracked back intimefor6days.Every2h,theparticles ’ three-dimensionallocation,the mixing layer height, the precipitation rate, and the SR werestored.TheseairmasshistorieswerethenusedtosolveEq.(2)fortheTCconcentrations and Eq. (4) for the source contributions from thedifferent source types. The particles ’  initial concentrations were setto 0, since modeling simulations showed that on average less than2% of the initial concentrations for 6-day trajectories arrived at thereceptor. The residence time  D t  0 in  was set to the trajectory segmenttime length of 2 h. If the particle was below the mixing layer, theemission rate  _ q in  was set equal to the 24-h area source normalizedbythemixinglayerheighttoconverttovolume source,else  _ q in  wasset to 0.The emissions added to the particle ’ s mixing ratio were froma weighted average of the emission grid cell in which the particleresided and the neighboring cells. The weights were from a two-dimensional Gaussian kernel where the bandwidths were basedon the horizontal spread due to turbulent diffusion. This is similarin concept to Gaussian averaging kernels used in forward LPDMs(de Haan, 1999) and allows for fewer particles to be used in thesimulation, with the same precision in particle counting statistics.As discussed in the Supplementary information, the countingstatistical error in the TC accounted for less than 2% of the totalmodeling error.The transmission function  p in  was calculated by integrating therate Eqs. (5) and (6) along each particle ’ s trajectory with the ratecoef  fi cient parameterized as discussed in Section 2.4.Speci fi cally, wet deposition was applied to all particles thatencountered precipitation, regardless of height, and the washoutdepth  H  w  was set to 1000 m. The TC washout ratio was  fi xed at 10 5 (Eq. (10)), based on the review from Bidleman (1988), and the VOC washout ratio was  fi xed at 3.5    10 4 (Eq. (11)), the average valueestimated from the CAMx model results.Dry deposition occurred if the particle was below the mixinglayer height. The VOC  v gd  was based on the results in Fig. 2 where  v gd Fig. 2.  Scatter plots showing the relationship between the average diurnal cycle in theeffective VOC dry deposition velocity derived from CAMx and solar radiation for January, April, July, and October. B.A. Schichtel et al. / Atmospheric Environment 61 (2012) 361 e  370  365
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