JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 100, NO. D12, PAGES 26,191-26,209, DECEMBER
20, 1995
The Regional Particulate Matter Model 1. Model description and preliminary results Francis S. Binkowski • AtmosphericSciencesModelingDivision,Air ResourcesLaboratory,National Oceanicand Atmospheric Administration,ResearchTriangle Park, North Carolina
Uma
Shankar
MCNC, ResearchTriangle Park, North Carolina
Abstract. The RegionalAcid DepositionModel hasbeen modifiedto createthe RegionalParticulateModel, a three-dimensional Eulerian model that simulatesthe chemistry,transport,and dynamicsof sulfuricacid aerosolresultingfrom primary emissions and the gasphaseoxidationof sulfur dioxide.The new model usesa bimodal lognormaldistributionto representparticlesin the submicrometersize range. In addition to includingthe horizontaland vertical advectionand vertical diffusionof the aerosol numberconcentrationand sulfatemassconcentrationfields,the model now explicitly treatsthe responseof the distributionparametersto particlecoagulationwithin and betweenthe modes,condensationof sulfatevapor onto existingparticles,formation of new particles,evaporationand condensationof ambientwater vapor in the presenceof ammonia,and particle-size-dependent dry deposition.The modelhasbeenusedto study how the degreeof sulfuricacid neutralizationby ambientammoniaaffectsthe total aerosolconcentrationsand particle size distributionsover easternNorth America. ß , ,:-' ...... •.• for thrcc representative•,,..•,• ........ •,,,,-,-,•, and nominal rremmna•y .,,........ , ..... 1, ..... ........... downwindof source,showthat the effectis greatestfor the rural and smallestfor the near-sourceregions,whichcorresponds with the largestand smallestvalues,respectively, of ammonium-to-sulfate molar ratios.The resultsindicatethat the model could provide a tool for investigating the effectsof variouspollutioncontrolstrategies,as well as new or alternativeformulationsof importantaerosolprocesses. gionalParticulateModel (RPM) isbeingdevelopedasa tool to investigatethis relationship. Particulatematter in the atmospherecan affectthe qualityof There have been several recent regional and subregional our livessignificantly becauseof its potentialimpacton human studiesof aerosolproductionand transportusingnumerical health and the environment.Aerosol particlesin the submi- models.Russellet al. [1983, 1985] useda trajectorymodel to crometersize rangecan be inhaledand thus may posecertain characterizethe nitrate aerosolin the Los Angelesarea; their healthhazards.Becauseparticlesin this sizerangealsoscatter work, however, did not include simulation of aerosol size dislight,theystronglyinfluencethe radiativebudgetof the Earth- tributions.Pilinis and $einfeld [1987] have publishedresults atmospheresystem;theyalsoreducevisibilityand diminishthe from a three-dimensionalEulerian photochemicalgas-aerosol recreationalvalue of national parks and other remote loca- model for the South CoastAir Basin of California, discussing tions. Several surveysof the current state of knowledgeof the aerosol chemistryin three broad-sizesections.Using a atmosphericaerosols[Finlayson-Pitts and Pitts, 1986;Seinfeld, three-dimensionalmodel developedby Toon et al. [1988], 1986;Warneck,1988]point towarda consensus that mostsub- Westphalet al. [1988] describedthe transportof Saharandust. micrometerparticlesare formed by gas-to-particleconversion They used30 sectionsto representthe sizedistributionbut did processes in the atmosphere.Further, in the easternhalf of not considerparticlecoagulation.Becausethe particlesof inNorth America, this size range appearsto be dominatedby terestwere larger than the fine-particlerange,the researchers sulfates.Passageof the Clean Air Act of 1990 created strong foundthat coagulationdid not alter the sizedistributionfor the interest in the mathematicalmodeling of how atmospheric casessimulated.Giorgi [1986] developedthe Atmospheric aerosolsbehave and their relationshipto both natural and AerosolModel for includingaerosoldynamicsin the National anthropogenicsourcesof sulfur and other species.The Re- Centerfor AtmosphericResearchCommunityClimateModel. His work usedanalyticsizedistributions (calledmodes)similar to the RPM's but considered coagulation only within the •On assignment to theU.S.Environmental Protection Agency,Na- modes,not betweenthem. Kftz [1991] and Kftz et al. [1991] tionalExposureResearchLaboratory,ResearchTrianglePark, North usedthe EuropeanAcid Depositionmodel (EURAD), a verCarolina. sion of the Regional Acid DepositionModel (RADM), to Copyright1995by the AmericanGeophysicalUnion. developa model similar to the RPM but without aerosolsize distributions.The Denver Air Quality Model (DAQM), anPapernumber95JD02093. 0148-0227/95/95JD-02093505.00 other extensionof the RADM, alsoincludesonly aerosolpar1.
Introduction
26,191
26,192
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MODEL
ticle massbut containsmanymore species.It is beingapplied over an urban domain with a grid resolution of about 8 km [Middleton,1993].
cles,dependingupon its concentration[Middletonand Kiang, 1978].Nitrate aerosolproductionalsoincreasesaerosolmass. HNO 3 vaporis a by-productformed duringthe photochemical In this contribution we describe the model's main characterproductionof ozone.If sufficientNH 3 is presentin the atmoisticsand current status.We then discussthe responseof the sphere,the H2SO4 maybe neutralizedto (NH4)2SO4,and any sulfateaerosolwater fraction(definedas the ratio of water to residual NH 3 may then combine with the HNO 3 to form total aerosolmass,namely,sulfateplusammoniumpluswater) NH4NO3 aerosol.The chemistryof the NH3-H2SO4-HNO3to neutralizationby ammonia.Finally, we discussfuture work. H20 systemis treated in the RPM by a modificationof the In part 2 (F. S. Binkowskiand U. Shankar,manuscriptin Model for an AerosolReactingSystem(MARS) of Saxenaet preparation,1995) we intend to presentresultsfrom simula- al. [1986]. tions usinga new schemefor accountingfor cloud scavenging MARS is an equilibriummodel basedon fundamentaltherand wet depositionof aerosolparticle distributions. modynamics.To minimize the number of equationsto be solved,the treatment of chemicaland interfacial equilibria focusesonly on major speciesfor each given set of ambient 2. Model Description conditions.The speciestreated in the MARS includeHNO3, SO42-, HSO•-,NH•-, Using experiencegained during the National Acid Precipi- NH3,andH20 in thegasorvaporphase; tationAssessment Program(NAPAP) [Binkowski et al., 1990], NO•-, H +, and H20 in the liquidphase;and H2SO4,with its we designedthe RPM utilizing the gas phasechemistryand increasinglyneutralized ammonium salts such as NH4HSO 4 transportmechanismsof the RADM, a comprehensive, three- and (NH4)2SO4,and HNO3 with its neutralizedsaltNH4NO3, dimensional,Eulerian air quality model [Changet al., 1990]. in the aerosolphase.Not all of thesespeciesmaybe presentin The RPM includesnot only all of the RADM mechanisms but a particularaerosol-gasequilibrium.The relative proportions presentaredictated bytheratioof NH•- to SO42alsothe chemistry,transport,and dynamicsof aerosolparticles of thespecies [Shankarand Binkowski,1992].The governingequationof the (i.e., the degreeof neutralizationof aqueousH2SO4), relative RADM is the conservationequationfor the chemicalconcen- humidity, and temperature. For example, for a given set of concentrations, the aerosolmay be a liquid or a solid;and for tration, C•, of speciesl: another, the aqueousphasemay be devoid of NO•-. Another important considerationis the relative humidity of deliques-
Ot....
• (bC3 + otI
+ Ot/
Chem
(la)
cence for the sulfate and nitrate
salts.
The distinguishingfeature of the original formulation of MARS is its divisionof the entire regime of aerosolspecies into severalsubdomainsin ambient relative humidityand the
(c]CT• •-(RIP*){PlmlCl qAwlDwl qEl} (lb)molarratioof NH•- to SO42-.Whilewehaveretaineditsbasic 0t / Chem = (n,e*)c, where the symbolsare defined in the notation section. The first two termson the right-handsideof (la) represent the horizontaland vertical advectionof the speciesconcentration by the wind field. The third term representsvertical turbulenttransport.For convectiveconditions,the modelusesthe AsymmetricConvectiveModel (ACM) of Pleim and Chang [1991]; for other atmosphericconditions,it usesa K theory
approachdueto Hasset al. [1991](seealsoByun[1990,1991]). The fourth term representsproductionor lossof the species due to chemicalreactions,wet deposition,and direct input from emissionsources. Theseare givenexplicitlyin (lb), where the right-handside terms in the bracesare, from left to right, the rates of gas phase production, gas phase loss, aqueous phase production, wet deposition, and source emissionfor speciesl. The term in the parenthesesconvertsthe concentration from molar mixingratio to massmixingratio multipliedby P*, as required for transport in the (r coordinate system [Changet al., 1990].Dry depositionis representedin the model as a boundarycondition on the finite-differenceform of the vertical turbulent-transportterm. Note that becausethis is a regional-scalemodel with horizontalgrid spacingof 80 km in the presentversion,turbulenttransportis accountedfor only in the vertical
2.1.
direction.
Aerosol Chemistry
Atmosphericsulfateaerosolis producedwhen hydroxylradicals oxidize SO2 in the presenceof water vapor to yield H2SO4,which either nucleatesor condenseson existingparti-
structure,we have completelyrevisedthe data used in calculating the liquid water content(LWC) of the aerosol.In calculatingthe LWC, we assumethat an ambientaerosolover the easternportionsof the United Statesand southernCanada is mostprobablyin the metastablestate(aqueousdroplets),that is, the relative humidityis greater than that for crystallization but lessthan that for deliquescence[Roodet al., 1989;Spann and Richardson,1985]. Thus we have ignored the effectsof deliquescence and hysteresis for aerosoladjustmentto relative humidity.Our argumentfor this is that when H2SO4 is formed throughthe oxidationof SO2by hydroxylradicals,the process alwaysoccursin the presenceof water vapor. This H2SO4 solutionis hygroscopic and adjustsvery quicklyto the ambient relative humidity, leading to an aqueous aerosol droplet, whetherby direct nucleationor by condensationupon an existingparticle.NH 3 moleculesthen bombardthe aerosolparticle, and the processof neutralizationcommences.This process differs from the laboratory system, in which a dry ammoniumsalt particle is humidifiedto deliquescence and a solutiondropletis formed.Spannand Richardson's [1985]experiment representspart of this processby beginningwith NH4HSO4 and adding more NH 3 to further neutralize the sulfate. However, they reduced the relative humidity low enoughfor crystallizationto occur. In the atmosphere,neutralization takes place under ambient conditions.The main point is that unlessthe atmosphericrelative humidity is lowered to that of crystallization,the particleremainsliquid during the entire neutralizationprocess. To illustratethis point further, at nightwith a surface-based temperatureinversion,verticaltransportof NH 3 (emittedfrom the groundsurface)is inhibited,and surface-layerconcentra-
BINKOWSKI AND SHANKAR: REGIONAL PARTICULATE tions can increase
with
time.
This
increase
means
that
the
probabilityof an NH 3 moleculestrikingan aerosolparticle is enhanced,leadingto further neutralization.During thisperiod of fallingtemperatures,relativehumidityincreases.During the day, when photochemical oxidation of SO2 leads to H2SO4 formation,NH3 is transportedover the much deeper surfacebased mixing layer, and the probability of neutralization is diminished.Relative humidity decreasesduring the day, but the aerosolsin the surface-based mixing layer are also transported, and as they rise they encounterdecreasingtemperatureswith increasingrelativehumidity.We would thus expect crystallizationto occuronly under very arid conditions.Hence we assumethat the aerosolsare alwaysin a wetted statewhen relative humiditiesare greater than that for crystallization.
experimentalwater activitiesreportedby Spannand Richard-
26,193
mode representsagedparticles.The particle dynamicsof this aerosoldistributionare describedfully by Whitbyet al. [1991]; therefore only a brief summaryof the method is given here. Given a lognormal distributiondefined as N
exp n(InD)= (2rr)•/2InO-g
-0.5
InO-g
(2)
whereN is the particlenumberconcentration, D is the particle
diameter,andD g and rrgthe geometric meandiameterand standarddeviationof the distribution,respectively,the kth moment
of the distribution
is defined
as
M•=•••D•n(lnD) d(lnD) (3)
In order to calculate the aerosol LWC, we used a fit to the
son[1985]for H20-to-SO42molarratiosasa functionof the NH•--to-SO42molarratio.For wateractivities greaterthan
MODEL
with the result
M•:= ND•: g exp
those given by Spann and Richardson[1985], we used the experimentalresultsfrom Nair and Vohra [1975], Tang[1980], and Cohenet al. [1987].Thuswe fit the entire rangeof relative humidity(water activity)from crystallizationto near 100%. Currently, we follow the MARS paradigm that all ambient
In20-g
(4)
M o is the total numberof aerosolparticleswithin the mode suspended in a unit volumeof ambientfluid (air). For k = 2 the moment is proportional to the total particulate surface NH3 isconverted to NH•- upto anNH•--to-SO42molarratio area within the mode per unit volume of air. For k = 3 the of 2.0 (fully neutralizedsulfate).Whereasthis is likely to be a moment is proportionalto the total particulatevolumewithin goodapproximationfor molar ratios of 1.5 or less,the results the modeper unit volumeof air. The constantof proportionof Spannand Richardson[1985]showthat the approachto full ality betweenM 2 and surfacearea is rr; the constantof proneutralizationby the additionof NH3 may slowdownfor molar ratios closerto 2.0. In particular, their resultsshow that the crystallizationcurvedoesnot approachthe samevalue of relative humidity as their own previouswork [Richardsonand Spann, 1984].Aurian-Blajeniet al. [1992] and Koutrakisand Aurian-Blajeni[1993]alsohavepresenteddata showingincomplete neutralizationof sulfuricacid for molar ratios between 1.9 and 2.0. Furthermore,Harrisonand Kitto [1992]report that atmosphericobservations showa reductionin the rate constant with acidicsulfatewith decreasingaerosolacidityfor the re-
actionof ammonium.Seinfeld[1986]showsthat [NH•-] is an increasing functionof [H+], that is, the more acidicthe solution, the more NH 3 goesinto solution.As a consequence,our currentratesof neutralizationof H2SO4 are likely to be overestimates
for the near-neutralized
scale that
extends
the
molal
ion interaction
modelof Pitzer[1987,1991]to verylow humiditiesand to fused aerosolparticles.We intendto incorporatetheseadvancesinto the RPM in the future. Also, for the work presentedhere we
assumed thatthe aerosolconsists entirelyof SO24 -, NH•-, and H20. This simplifiedsystemwasusedas a modeldevelopment platform. Consequently,we have consideredneither nitrates nor organicand elementalcarboncomponents. As we improve the aerosol phase chemistryof the model, these additional specieswill be included. 2.2. Aerosol Dynamics
moment
is selected. Prediction
of three moments
of the distri-
bution functionwill allow both the geometricmean diameter
D g andgeometric standarddeviationrrgto be diagnosed as functionsof time [Whitbyet al., 1991]. Letting the nuclei and accumulation modesbe representedby subscripts i andj, respectively,the rate equationsfor the kth aerosolmoment for these two modesare given by
o
( 1
+ Gk,+ Ck, + C•o + E•i
(5a)
aerosols.
Finally,the MARS paradigmis basedupon a molal (moles of solute per kilogram of water) concentrationscale,which becomesincreasinglyinaccurate as aerosol LWC decreases with decreasingrelative humidity.Recent work of Clegget al. [1992] and Cleggand Pitzer [1992] arguesfor a mole fraction concentration
portionality between M3 and volume is ,r/6. Note that the geometric standard deviation is the same no matter which
OM• 07s= - V'(VMkj) - •O(bM•j) + -•-?DiS + G•s+ C• + Ckji nt-E•
(5b)
Although the choiceof the value for the indexk is arbitrary and can includenonintegervalues,for reasonsof mathematical simplicitythe currentversionof the modelhastime-dependent equationsfor the zeroth, third, and sixth momentsof the distributionfunctionsfor eachsizemode.Thus(5a) and(5b) each representsthree equationscorrespondingto valuesof k equal to 0, 3, and 6. The form of these equationsis similar to the speciesconservation equation,(1). That is, the firstthree terms on the right sideof (5a) and (5b) representtransportof the kth aerosolmomentby the horizontalwind, the verticalwind, and turbulent diffusion,respectively.The same commentsapply aboutthe useof K theoryand the ACM here asfor (1). Only the aerosol number moment, correspondingto k -- 0, is transported for both modes. The aerosol volume moment, which is proportionalto the third moment (k = 3), is constructedfrom the massconcentrationof the particle constitu-
The aerosolparticle size distributionis modeled upon the conceptsdevelopedby Whitby[1978].The particlesare divided into two size ranges,or modes.The smaller (nuclei) mode representsfresh emissions,while the larger (accumulation) ents(SO24 -, NH•-, andliquidH20) by dividing bytheappro-
26,194
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AND SHANKAR:
REGIONAL
PARTICULATE
MODEL
priatedensities. SO42-andNH•- aretransported, whileliquid quiredfor the production of 1 particlecm-3. Kerminen and Wexler[1994] have deriveda simplealgorithmfor nucleation from an extensionof the work of Middletonand Kiang [1978]. Our implementationof this algorithmis shownin the appendix. Becausesimple, accurateparameterizationsfor particle productionprocesses in point sourceplumesare not yet available in a form suitable for the regional scale, only a crude representationof new particles resultingfrom the primary emissionsof sulfate is includedin this first-generationmodel; this representationis describedin section2.5. Aerosol growth by condensationoccursin two steps:the 2.3. Coagulation productionof condensablematerial by chemicalreaction,and Aerosol sizedistributionscanbe alteredby particlecollision the condensationand evaporationof ambientvolatile species and coagulation.In general,the mathematicalrepresentation on aerosolparticles.The productionof condensablesulfate of coagulationpresentsformidable difficulties.If, however, resultingin stableparticleswith increasingsizesis represented only coagulationby Brownianmotion is considered,the prob- explicitlyin the RPM. The inclusionof secondaryorganicand lem simplifiessomewhat[Friedlander,1977;SeinfeM,1986].If nitrate specieswill be treated in a subsequentcontribution. the particledistributionremainslognormal,the problemsim- The growth rates for stable aerosolparticlesdue to vapor plifiesfurther [Whitbyet al., 1991].As describedin the Appen- condensationare derivedin the appendixand are givenby dix, the integralsrepresentingBrowniancoagulationof particleswithin eachmode and betweenthe modesare represented • (7a) as harmonicmeansof the coagulationcoefficientsin the freemolecularand near-continuumparticle sizeregimes.Analytical expressions for thesetwo regimesare givenby Whitbyet al. [1991].Without seriouslossof accuracy,this harmonicmean approachusinganalyticalexpressions allowsmuch more effi- M 3 is the rate of increase of M3 dueto condensation andis cient calculationof the coagulationtermsthan would be pos- givenby sible using, for example, numerical quadrature as done by i•3----(6/7r)(Cl/Pl) (8) Giorgi [1986]. Thus the two intermodal terms for coagulation betweenparticlesfrom modesi andj are givenby whereC• isthechemical production rateof species l andr• is fmt•nc its density.Note that the growthrate for M o is zero; that is, the kij •.-•kij Cktj: •'fm •'nc (6a) number of particlesdoesnot changewith the addition of conCk,;+ Ckij densingmass.The other terms are discussed more fully in the fmt•nc appendix. lqt • l•ji Water is the most important volatile speciescondensing Ckji-- "fm nc (6b) C•;•+ (•;, uponand evaporatingfrom atmosphericaerosols.The swelling Intramodal coagulationbetween particles within mode l, and shrinkingof particleswith changesin relativehumidityis a well-established phenomenonand is discussed fully by Hiinel where l denoteseither mode i or modej, is given by [1976] and Pruppacher and Klett [1978]. Pilinis et al. [1989]show fmt•nc kll •kll that this swelling and shrinking of particles is an equilibrium Ckll-- •'fm •'nc (6c) C•tt + C•t• process.In view of this, the adjustmentof M 3 to relative humidity is modeled as an equilibrium calculationusingthe These expressions are derivedand discussed in the appendix. increaseor decreaseof liquid water content specifiedby the aerosolequilibriumchemistrymodule discussedabove,recog2.4. Nucleation and Growth nizing that Mo is not affectedby this changein particle size. Nucleation,or new particle formation, and growth of exist- Becausethe amount of water presenton an aerosolparticle at ing particlesby condensation of vaporare the two pathwaysfor a givenrelativehumidityis directlyproportionalto the massof increasingthe total aerosolmass.Middletonand Kiang [1978] hydrophilicmaterial present,the condensationand evaporashowedthat either nucleationor condensationcanbe the prin- tion of water may be considereda mass- or volume-based cipalpathwaydependingupon atmosphericconditionssuchas growth process.For such a process,the geometricstandard temperature,relative humidity,the total aerosolsurfacearea, deviationO-gcan easilybe shownto be constant.Tangand the impingementrate of vapor moleculeson the particles,and Munkelwitz[1977]showthat a nearlymonodisperse dry aerosol the chemicalproduction rate of condensablematerial. For remainsnearlymonodisperse (withinexperimentallimitations) troposphericsulfateaerosols,binaryhomogeneous nucleation duringhumidificationto veryhighvaluesof relativehumidity, of sulfuric acid and water vapor appearsto be the primary givingrather strongexperimentalevidencethat the geometric nucleation mechanism.Easter and Peters [1993, 1994] have standarddeviationis unaffectedby the swellingof particlesin analyzedthis processin the contextof the marine boundary responseto increasingrelativehumidity.Thus our equilibrium layer and showthat rapid fluctuationsin the temperatureand adjustmentto relative humidityholdsthe geometricstandard relative humiditycan lead to burstsof particleproductionby deviationconstantand diagnosesM 6 accordingly. binary nucleation, especiallynear the top of the convective 2.5. Emissions mixinglayer. Wexleret al. [1994] have fit an empiricalexpression to nucleationrates given by Jaecker-l/oiroland Mirabel At presentthere are inadequatedata on the sizedistribution [1989] for the critical concentrationof sulfuricacid vapor re- of aerosolsemitted by sources.McElroy et al. [1982] have H20 is equilibratedlocally.The lastfour termsrepresent,from left to right, the changein aerosolmoment by condensational growth,coagulationof particleswithin the mode, coagulation of particlesbetweenthe modes,and sourceemissionof particles.Dry depositionof aerosolparticlesis taken into account as a lower boundaryconditionin the finite-differenceform of the turbulent diffusionterm. We discussthe dry deposition algorithmin section2.6 and describethe detailsin the appendix. The predictioncycleis alsodescribedin the appendix.
•
(7b)
BINKOWSKI
AND SHANKAR:
REGIONAL
PARTICULATE
MODEL
26,195
shown that coal burning yields aerosol emissionsin the size
rangeof thenucleimode.Whitby [1978]givesvaluesforDg and O-gfor a largepowerplant plumeand severalnear-source situations.In a regional model, emissionsare assumedto be mixed instantaneouslyinto the grid cell volume; therefore Whitby'snear-sourcevaluesare relevant.The rate of changeof aerosol volume
concentration
due to source emissions
can be
determinedfrom the aerosolspeciesmassemissionsrate E 1by dividing it by the speciesdensityPl. For the work reported here,El isthe emissions rate for sulfate(takenasH2SO4).The rate of changeof M 3 due to emissionsis
M3 = (6/rr)(El/Pl)
..... .... ,.... .... ....
(9)
The emissionsrate for aerosolnumber is given by
N=
(10)
D3g exp((9/2) In2O-g)
and that for any k moment is givenby
M•= ND•exp-2-In2rrg
(11)
We then assume
:::::::::::::::::::::::: ::::::::::::::::::::::::
(12)
Figure 1. Modeling domain. Selectedgrid cells are cell A (nominaldownwindof source),cell B (rural), and cell C (near source).
The fractional split of the emissionsbetween the modes is a crude representationof the growth of particlesoccurringin plumeswhich are not yet representedexplicitlyin the model.
sulfuremissions[Binkowskiand Shankar,1992a,b, c]. Results
E•, = 0.15M•
E•; = 0.85M•
Thevalueschosen for thesizes(Dg andrrgvaluesof 0.01/•m from this path are presentedin section4. The final stage of and 1.6 for the nuclei mode and 0.07 and 2.0 for the accumudevelopmentis the mergingof the two pathsinto a final model lation mode, respectively)correspondto the Whitby[1978] that has sulfate, nitrate, and organic aerosolsalong with the valuesfor local sourcesand background,as do the fractional size distributionsand aerosoldynamics.This will be reported aerosolvolumesin the nuclei and accumulationmodes(0.17 in future contributions. and0.83),respectively. This issuewill be revisitedwhenplumes
are representedexplicitlyin the model. 2.6.
4.
Preliminary Results From Two Model
Simulations
Dry Deposition
We will describe
the results of two model
simulations
over
We use a conventionaldepositionvelocityapproachfor dry the RADM domain shownin Figure 1 for a case, denoted as deposition;however,we applyit to the depositionof the zeroth the base case,usingthe 1985 emissionsused for the National andthird momentsof the ith andjth modesusingthe following Acid PrecipitationAssessmentProgramand for a secondcase, equation: denotedasb0, whichis identicalin all respects,exceptthat the ammonia
Vdk = Mki+
3
wherewe have assumeduniform particle densityin the caseof the third moment.The detailsof our approachare givenin the appendix.
3.
Model
Realization
To build a model as complexas the RPM within a reasonable time frame, a two-path strategywas chosen.First, aerosol chemistryas representedby the MARS modulewas added to the RADM to investigatethe model performanceand sensitivity to ammoniauncertainties[BinkowskiandAlapaty,1991]. In a parallel effort, we incorporatedthe Modal Aerosol Dynamicsapproachof Whitbyet al. [1991]into the TaggedSpecies EngineeringModel (TSEM) [McHenryet al., 1991]. This allowed us to develop the methods for dealing with volatile components,representedin this caseby water, and to investigate the behaviorof aerosolsizedistributionswith realistically varying humidity fields, as well as hypotheticalreductionsin
concentrations
are set to zero. These two simulation
casesmodel the role of ammonia in neutralizing the sulfate aerosol. For the two simulations
the aerosol is either a sulfuric
acidsolutiondroplet(b0) or a partlyto completelyneutralized sulfatesolutiondroplet(base),dependinguponthe molarratio
of NH•- to SO42-.The simulations are for an atmosphere in which cloudsare ignored except for attenuatingsolar radiation. Further, no speciesof particlesother than sulfateaerosols are considered.
We presentthe resultsas time historiesfor the lowestof the 15 model layers in three grid cells shown as A, B, and C in Figure 1. This layer is about 80 m deep. Cell C represents near-sourceconditions,cell B representsrural conditions,and cell A representsnominal downwindconditions.Other than trying to representa wide range of emissions(i.e., rural to urban-industrial),the choiceof cellsA, B, and C wasarbitrary.
Figure2a displays theemission ratesof sulfur(SO2andSO•-, taken as H2SO4);Figure 2b showsNH 3. Both setsof emission rates(in kilogramsper hectareper day) are for a typicalsummer weekdayand are plotted from data givenby Changet al. [1990].Theseplotsshowthat most of the large sulfursources
26,196
BINKOWSKI
AND SHANKAR:
REGIONAL
PARTICULATE
MODEL
0.3
............ ......... ............ ........ ........... .........
............
:Xl:X::X ::x::x::
o.5
:x::x::x ::x::x:: :x::x::x ::x::x::
0.1
0.05
0,02
.::.:0.018 ...
... ß
.
:i::::i. 0.016 i:i:i: ......
:::.:: :,:::,. .......
!•:-•:0.014
:............... o. o1 0,008
:x:: ::x: -x:: ::x: -x::
"•'-0.006 ....:.
7::: ,:,% ,,
/,ø% ,o,
0.004 0.002
b Figure 2. Daily total (a) sulfur(SO2 + SO4) and (b) ammoniaemissions(kilogramsper hectareper dayfor a summerweekday(1985 NAPAP data from Changet al. [1990]).
BINKOWSKI AND SHANKAR: REGIONAL PARTICULATE MODEL
ß
i
'
'
26,197
•
\
'
..
Xl
l/ N...... •'•-7••-• • ..... :' .... ! k1'•-'i-.... 2x- • k ;Jl • [/, ....•,....•'"2•_'
I(••i:'-g
.....
.,
,'-
.....
-v
,,,
t ...... -"-i"- • •
,
.-r-r>'',"
•
ß ¾';'• •
-"J•.
•x
,
::.?a•,•' • ,/V.T'= -'•i(_B•g•...-• ' •.•.1 ••t•f':i .•..>....rV,•
•. !f il •....• •(I•
• ""xp'
"'•'"z,•=•............. ) •:[ •'•:1"z•!• ...... • .....
) ri•,re 3. W•ath•rmaps for(a)0000UT,July1Z 198•,hour00ofth• simulation; (b)0000UT,July18, 198•,hour24ofth• simulation; (c)0000UT,July19,198•,hour48ofth• simulation; and0000UT,July20, 198•, hour I2 of th• simulation.
[1978]for thenumberdistriare eastof the main ammoniasources.This impliesthat am- 2.0for modej (givenby Whitby tocalculate theothermoments. Thesevalues areused moniamustbe transported to thesulfursources if thesulfates butions)
(bothemitted andchemically produced) aretobeneutralized.to
calculate the aerosol number and sixth-moment concentration emissions rates from the sulfate mass emission rates.
Thispointis addressed furtherbelow. meteorological casefrom Placetet al. [1990]describethe NAPAP 1985 emissions We chosea typicalsummertime inventory. The anthropogenic emissions are time-dependent,the ensembleof casesdevelopedfor the NAPAP work etal., 1990].The72-hour simulation beganat 0000 andthe ratesarebaseduponengineering estimates of operat- [Binkowski
ingcycles. Naturalor biogenic emissions are modulated by UT onJuly17,1985(Figure3a)andendedat0000UT onJuly dryanddominated atmospheric conditions. Detailsof howtheNAPAPemissions20 (Figure3d).Thisperiodwasrelatively system passing through themodeldomain. areincorporated intoRADM aregivenbyChang etal. [1990]. bya high-pressure The RPM followsthe RADM usageexceptas alreadynoted. Betweenhours36 and48 of the simulationperiod(Figures3b
through cellB, andrainfellfrom The boundaryand initialconditions for chemicalspecies and3c),a coldfrontpassed concentrationsare the same as those used in the RADM and
about hour 40 onward.The winds at cell B were southeasterly
andthensoutherly priorto the frontalpassage, afterwhich theybecame northerly. ThewindsatcellsA andC werenorthuntilthecenterof thehighpassed to theeastbyhour limits the influenceof both meteorological"spin-up" and easterly chemical equilibration effectson the periodunderstudy.For 36. Rain fell in cell C from about hour 63 onward. There was period.Figure4 initialandboundaryconditions on the aerosolsizedistribu- no rainin cellA duringthe entiresimulation timeseriesplotsof gridcellaverage relativehumidity in tions,the initial sulfateconcentration is dividedby an average shows each of the three grid cells. These humidities are consistent density of 1.8g cm-3 to obtaina volumeconcentration. Using valuesfromWhitby[1978],we splitthe sulfatevolumeconcen- with the weathermapsin Figure3. Note that the highest is in cellB aftertherainstarted. Thesemeteorologtrationbetweenmodesi andj by a fixedfractionof 0.01 and humidity bya mesoscale numer0.99,respectively. We thenuseinitialvaluesof D g and Crg, icalinputsfortheRPMwereprovided ical weather prediction model (MM4) using four-dimensional respectively, of 0.01/xmand1.7for modei and0.07/xmand
TSEM simulations. Thusthe simulationperiodpresentedhere consistsof the last 72 hours of a 120-hour simulation. This
26,198
BINKOWSKI AND SHANKAR: REGIONAL
PARTICULATE
MODEL
We now discuss the results for chemical concentrations
90
and
related information.Figure 6 showsthe temporalvariationsof
85
the SO42-and SO2concentrations. There are no differences between
8O
these concentrations
for the base and b0 cases. For
• 75
the first 36 hours, the sulfate concentrations in cells A and B
.• 70
southwesterly flow beginsat cell A between36 and 72 hours,
:3 65
E
theSO]- concentration increases to 13 tagm-3, whichis less thanhalfthatin cellC (36tagm-3), a veryhighemission area.
ß 60
The SO2concentrationincreasesand peaksat a value of 35 tag
-• 55
m-3 at hour60.The sulfatein cellA increases partlybecause
arecomparable andlessthan10tagm-3. Afterthesoutherly to
.>_
of transportfrom the major sourceregionto the southwestand partlybecauseof the increasedproductionshownin Figure 5. Thisviewis supportedby the increasein SO2betweenhours48 45 and 60, which correspondsto a minimum in local emissions 40 (Figure5). The peakat hour60 is dueto the morningpeakin 0 12 24 36 48 60 72 emissions.During this same time interval the sulfate concenHour trations in cell B decreasedue to the postfrontalnortherly wind transportingcleaner air. This is seen also in Figure 5, Figure 4. Relative humiditiesfor cellsA, B, and C. wherethe productionrate of sulfatedecreases duringthistime. Although the meteorologicalinformation indicatedrain, wet data assimilation[Staufferand Seaman, 1990; Staufferet al., depositionis not activein the presentsimulations. During the first 12 hours of the simulation,the concentra1991]. As expectedfrom the discussion of Figure 2, the emissions tionsof sulfatedecreasein all three cells.This is unlikelyto be ratesshown in Figure5 for SO2(SO2E)andSO42(SO4E)are an equilibrationproblem,becausethe initializationprocedures highestin cell C and lowestin cell B, with the emissionratesin developedas part of the NAPAP effort mitigatethis effect.It cell A havingintermediatevalues.The productionratesin cell appearsto be a resultof the passageof an essentiallycleanair A increaseoverthe simulationperiod;thosein cell B decrease. massacrossthe region.The sharpdecreasein sulfateconcenThe cloudinessand rain occurringafter hour 40 diminishedthe tration in cell C between hours 36 and 48 is associated with the gasphasechemical production of SO42-.Thissameeffectis sharpincreasein dry depositionshownin Figure 7. There is seen in cell C after hour 63. Note that the resultspresented also a sharp increasein sulfur dioxide concentrationsat the here do not include the effectsof any cloud or aqueouspro- same time. The behavior is repeated, althoughlessstrongly, cessesother than the inhibition of gas phase production of just after hour 60. In cell A after hour 60, dry deposition while production(Figure5) decreases; yet the conhydroxylradicalsto oxidizethe SO2.Evenwith thisdiminution, increases, 50
thechemical production rateof SO,•-ismuchlargerthanthe centration continues to increase. This is consistent with the emission ratefor SO42-.Note thatin cellB thechemical pro- interpretationthat part of the increasein concentrationof ductionof SO42-exceeds the emission rate of SO2between sulfateis due to transport. hours 12 and 24. The transientsin the emissionrates occurring Ammoniumto sulfatemolarratiosfor the basecase(Figure in the morning and eveningare causedby the interactionof 8) showa strongdiurnalvariationin all three cells,with nightplume rise with the depth of surface-based turbulentmixing time maxima.The large transientin this ratio for all three cells during the first 12 hours is due to the decreaseof sulfate [Byunand Binkowski,1991].
Cell C
-
'!I
'.• lO0
• 10'2
•1
10'4
...... 0
ø
12
24
36
48
60
72
0
12
24
36
48
60
72
0
12
10 '2
•.....•.....•.....•.... 10'4 24
36
48
60
72
Hour
Figure 5. Emissionrate for SO4 (SO4E), SO2 (SO2E), and gasphasechemicalproductionrate for SO4 (SO4P). Units are microgramsper cubicmeter per hour.
BINKOWSKI
AND SHANKAR: REGIONAL
PARTICULATE
MODEL
26,199
120
Cell A
Cell B
lOO
-
100
=
,
.
80
.
60
-
60
40
-
40
20
-
20
0
12
24
36
48
60
72
0
12
.
SO2
=,=•=
SO4
24
36
48
8O
60
72
0
12
24
36
48
60
72
Hour
Figure 6. Sulfate(SO4) and sulfurdioxide(SO2) concentrations (microgramsper cubicmeter). Both base and b0 cases are the same.
concentrationsfrom the initial conditions.Our interpretation is basedupon the understandingthat ammoniais emitted from the surfaceand transportedverticallyby turbulent eddies.At night these eddiesare usuallyweak, and ammonia concentrations can increaseat lower altitudes(say, in the lowestgrid cell). With the initiation of daytimethermal convection,ammonia is distributed over a deeper layer, with a consequent
2:1 indicatesfully neutralizedsulfate(ammoniumsulfate)and is present during the first 12 and last 3 hours in cell B. The particlewater massfraction(Figure 9) resultsfrom an equilibriumbetweenthe aerosolparticlesand relative humidity [Piliniset al., 1989].The amountof water presentis determined by the ammoniumto sulfateratio. Thus the water mass fraction is quite different for the base and b0 cases.Cell B decrease in concentration. Sulfate concentrations do not show showsthe most strikingdifference.The curvefor the basecase sucha pronounceddiurnal variation becausesulfate is a sec- is seento be strongly(inversely)relatedto the molar ratio plot ondaryspecies(i.e., the formationof sulfateis mainlydue to for cell B in Figure 8. Cell C showslittle or no difference the oxidation of sulfur dioxide, which dominates over the direct
between
emissionof sulfate,as seenin Figure 5). The molar ratios are largestin cell B, which is in the heart of the ammonia source region (Figure 2b). The molar ratio in cell C is the smallest becauseof the largesulfursourcesand smallammoniasources. The valuesin cell A are intermediate and, in addition to the strongdiurnal behavior,displaya trend inverseto the sulfate concentrations shownin Figure 6. Note that a molar ratio of
the very smallvaluesof the molar ratio in Figure 8. The initial transient in molar ratio in Figure 8 for all three cells is reflected
the base and b0 cases after hour 24. This is related
in the minimum
differences
in water
values in water
mass fraction
mass fraction.
are associated
with
to
These differ-
encesin averageparticledensity(Figure 10). Minima in water massfraction are associatedwith maxima in averageparticle density.Note that there is alsoa differencein averageparticle
0.2
Cell A
0.18
-
Cell C I 0.18
Cell B
.
,•
0.16
d
0.14
'"
0.12
0.16
0.14
dd(b)-base
0.12
=--,=,, dd(b)-b0 'o
0.1
•o
0.08
0.1 0.08
C3 0.06
0.06
C3 0.04
0.04 0.02
0.02
0
0
12 24 36 48 60 72 0
12
24
36
48
60
72 0
12
24
36
48
6O 72
Hour
Figure 7. Dry depositionof particles(dd, kilogramsper hectare)for the base and b0 cases(the curves overlap).
26,200
BINKOWSKI
AND SHANKAR: REGIONAL
PARTICULATE
MODEL
13,whichshowsplotsof the steadystateconcentrationCss,and the criticalconcentration Ccrit(both are definedin the appendix) for eachof the threegrid cells.In cellA, newparticlesare
2
o 1.8 n- 1.6
formed around hour 12 and hour 36. In cells B and C, new
•o 1.4
particles are formed around hour 12. Regional maps (not shownhere)of the occurrence of nucleation(Cssexceeds Ccrit) indicatethat there is a broad geographicregion of occurrence in grid cellslyingbetweencellsA, B, and C duringhours12 to 20. During hours36 through42, a regionof nucleationextends east and north of cell C. During hours 60 through 66, the region is again to the east and north of cell C and smaller in extent than on the previousday. It would seemthat the pro-
(• 1.2
'5
1
o 0.8 E
= 0.6
o 0.4 E E
duction
rate of sulfate exceeds the condensation
rate for most
of the daylighthourson the first 2 daysand that thesenew
< 0.2
particles are transportedto cells C and A. There must be transportto cell C becausethere is no nucleationin this cell after hour 48, but the number concentrationof i mode particles(Figure 12) increases,and there is strongdry deposition (Figure 8). The numberconcentrations in Figure 12 are generallywithin the rangeof valuesreportedin Table 1 of Whitby [1978].The rangefor cell C, however,is somewhatlarger than Whitby'sbackgroundand local sourcescategory.This is to be expected,sincethe omissionof cloudsand aqueousproduction of sulfateremovesa mechanismfor addingmassto thej mode.
o
o
12
24
36
48
60
72
Hour
Figure 8. Ammonium to sulfate molar ratios for cellsA, B, and C for the basecase.This ratio is uniformlyzero for the b0 case.
refractive index associated with water mass fraction, with
higher values of water mass fraction being associatedwith smaller refractive indices;that is, the curvesof averagerefractive index should behave like the curvesfor averageparticle density.This meansthat the level of neutralizationof sulfate has importantoptical effects[Binkowskiand Shankar,1992b]. The total particlemassconcentration(Figure 11) is similar
This in turn reduces the total surface area for condensation
of
mass produced by gas phase chemistryand shifts the mass producedto the i mode via new particle production. In Figures14 (basecase)and 15 (b0 case),we seethe size distributionsof particlemassfor six 12-houraveragingperiods ending at the hours shown.This was accomplishedby conto that of sulfate but shows differences between the base and structingthe distributionshourly and averagingthesedistribub0 cases.As expectedfrom the discussionthus far, the differ- tions over 12-hour time intervals.This proceduremimicsthe encesare the largest in cell B and smaller in cells A and C. currentobservationalpracticeof collectingsurface-based samModel simulations(not shownhere) in whichnucleationwas ples of particle distributions.ComparingFigures 14a and 15a, omittedpartitionedthe new massgeneratedby sulfateproduc- we see that peak valuesfor the averagedtotal massdistribution between the modes, causingthe j mode to grow. In the tions for the period ending at hour 72 in cells A and B are model results reported here, nucleation is in effect and, as slightlylarger in the b0 casethan in the basecase.Note also describedin the appendix,the new particlesare distributedin that for both the base and b0 cases the distributions become the i mode. Thus the massrepresentedby the newly formed narrowerand peak at smallerdiametersin cellsA and C, while particlesincreasesthe i mode massand number(Figure 12). in cell B the distributions broaden with time and retain more of To better illustrate this shift in mass,we now discussFigure a bimodal character. Figures 14b and 15b show the sulfate
1
0.9
CellA
Cell (•
Cell B
0.9
0.8
0.8
0.7
0.7
0.6
0.5
0.5
0.4 •03
0.4
wf-base 0.3
.
----- wf-bO
0.2
'0.1 Iiiiil,,,,,I,,,,,I,,,,,i,,,,,i,,,,l
0.1
0
.... I ..... I ..... I ..... I .... ,I,,,,,
.... I ..... I ..... I ....
12
24
36
0.2
48
60
72 0
12
24
36
48
60
72 0
12
24
36
48
60
Hour
Figure 9. Averageparticlewater massfraction(wf) for the baseand b0 cases.
0
72
BINKOWSKI
AND SHANKAR:
REGIONAL
PARTICULATE
MODEL
26,201
1.6
1.6
Cell A 1.5
1.5
1.4
1.3
1.2
1.2
1.1
1f,.... I..... I..... I..... I..... I.... o
12
24
36
48
60
72
o
ll,,I ..... I,,,,,I,,,,,I,,,,,I,,,, 12
24
36
48
60
72
0
12
24
36
48
1 60
72
Hour
Figure 10. Averageparticle density(gramsper cubiccentimeter)for the baseand b0 cases.
120
..... i ..... i ..... i ..... i ..... i ..............
Celia
(•;I;(•
I ....
120
100
100
80
80 .
60
60
40
40
20
20
0
0
0
12
24
36
48
60
72
0
12
24
36
48
60
72
0
12
24
36
48
60
72
Hour
Figure 11. Total particlemassconcentration(microgramsper cubicmeter) for the baseand b0 cases.
,•
106
106
r• 1
103
=
Ni
z
....e
.
•' 100....I.....i.....I.....i.....I........ 0
12
24
36
48
60
72
i.....i.....i.....i.....i.... 100 0
12
24
36
48
60
72
0
12
24
36
48
60
72
Hour
Figure 12. Particle number concentration(number per cubic centimeter)in i and j modes.Differences betweenbase and b0 casesare indistinguishable in this plot.
26,202
BINKOWSKI
AND SHANKAR: REGIONAL
PARTICULATE
MODEL
100
100
10-2
10-2
Css
0
12
24
36
48
60
72
0
12
24
36
48
60
72
0
12
24
36
48
60
72
Hour
Figure 13. Critical and steadystateconcentrations (microgramsper cubicmeter) for basecase.Thosefor the b0 caseare very similar. See the appendixfor definitionsand details.
,... 40
•,
[----•••r12 !•CelIB [ i I ....... Hr24
35
• 30
140 120
100
Q 25
'•
80
20
60
• 15
40
5 -o
0
0
0.01
0.1
1
10
0,01
0.1 Particle
1
10
0.01
0.1
1
10
Diameter
Figure 14a. Total masssize distributionfor the base case.Note scalechangefor cell C. The plots are for 12-hour averagesending at the time shown. ,..,
40
I
I
I I II III
I
I
I
I II
140
II I
Cell C
.
Cell ^
E 35
-
120
.
"-'
:
30
IO0
.
:
'•
25
o
'•
8O
.
:
20 -
•__
.
6O
15 4O 10 2O
5
0
0--
0.01
0.1
1 0.01
0.1 Particle
1
10 0.01
0.1
1
Diameter
Figure 14b. Sulfate masssize distributionfor the basecase.Note scalechangefor cell C. The plots are for 12-hour averagesending at the time shown.
BINKOWSKI AND SHANKAR: REGIONAL
PARTICULATE
4O
MODEL
26,203
........ • ........ • ........
140
Cell A
•.
-
I I
3o
120
IO0
I
cl 25 _9o 20 '-'
15
I I I I
80
6O
o
•
40
lO
(•
20
5 o
O.Ol
ß
0.1
1
10 0.01
0.1 Particle
1
10 0.01
0
0.1
1
10
Diameter
Figure 15a. Total masssize distributionfor the b0 case.Note scalechangefor cell C. The plots are for 12-hour averagesendingat the time shown.
massdistributionfor the baseandb0 cases,respectively.These plots were constructedassumingthat water removal does not
affectthe geometricstandarddeviations, O-g i and o-g/.Then "dry" diameterscan be calculatedand the sulfate massdistributions(includingammonium)constructed.ComparingFigures 14b and 15b, we seebehavior similar to that for total mass.
The sizedistributionsin Figure 14 and 15 are representative of the rather restrictive experimental conditions described above,that is, that we consideronly sulfate aerosolparticles. Gasphaseoxidationof sulfurdioxideis the solemechanismfor the productionof secondarysulfate.Cloudsare ignoredexcept for their
attenuation
of solar radiation.
The
result
of these
5.
Summary and Conclusions
We have developedan Eulerian model, the RPM, that provides a potentially important tool for investigatingtroposphericaerosolbehavior.By usinganalyticfunctionsfor aerosol size distributionsin two size rangesof particles,we have provideda computationallyefficientalternativeto the sectional approachon a regional scale.Incorporatingthe most important aerosolprocessesinto the RADM allows us to build a multipurposemodelingsystemthat has most of the relevant chemistryand physicsof trace gasesand aerosolsnecessaryfor mesoscalelower troposphericstudies.The model providesa platform for testing alternativeformulationsfor aerosolprocessesand their effectson aerosolconcentrationand deposi-
conditionsis that new particle productionby nucleationbecomesrelativelymore importantand the sizedistributionshifts to smallersizeswith time. Resultsof extendedwork [Binkowski tion. Model refinements discussed in the next section will enand Shankar,1994;Shankarand Binkowski,1994] not shown hance the applicabilityof the model to such environmental here, which includesclouds,confirmsthis interpretation.This problemsas the fate of semivolatileorganiccompoundsin the work will be fully reportedin a subsequentpaper. atmosphere,the responseof aerosolsto hypotheticalcontrol
4O
E
140
Cell A
35
120 .
.
'---' 30
IO0
25 8O
o
ß.o
2o 6O
4O
2O
0
0.01
0.1
1
10
0.01
0.1
1
10
0.01
0.1
1
10
Particle Diameter
Figure 15b. Sulfatemasssize distributionfor the b0 case.Note scalechangefor cell C. The plots are for 12-hour averagesendingat the time shown.
26,204
BINKOWSKI
AND SHANKAR: REGIONAL
strategies[Binkowskiand Shankar, 1992a, c], or the studyof the optical and radiative behavior of atmosphericaerosols [Binkowskiand Shankar,1992b]. This preliminary study showsthat the neutralizingcharacteristicof ammoniastronglyinfluencesthe aerosolLWC, and therefore the total aerosol volume concentration, because a
PARTICULATE
MODEL
scavengingby in-cloud mechanismscoagulatesaerosolparticleswith cloud water droplets, and rain removesthe material from clouds. We have extended
this method
to include
a sim-
ple parameterization of nucleation scavenging as well [Binkowskiand Shankar,1994;Shankarand Binkowski,1994]. Resultsof this work will be reported in part 2 of this paper.
molarratioof NH•--to-SO42greaterthan1.0results in a lower LWC at the same relative humidity. The resultsfor volume concentrationshowthat the strongestinfluenceis in the rural region, the next strongestin the downwind-of-source region, and the weakest in the near-source region. Because acidic particlespose a potential health hazard, neutralizationis an issuefor human health as well. The importanceof neutralization leads immediately to the corollary that better ammonia emissionsinventoriesare needed, along with a better understandingand formulation of the processof neutralization. 6.
Future
Work
A1.
Coagulation
Coagulationof particles is discussedfully by Whitbyet al. [1991]. The main points of the discussionare as follows.All coagulationof aerosol particles is in responseto Brownian motion. Aerosol volume is conservedduring coagulation;the volume of a particle resulting from the coagulation of two other particles is equal to the sum of the volumes of the coagulatingparticles.Thus the diameter of the resultingparticle is taken
As mentioned in section 2.1, future versionsof the RPM will
include secondarynitrate and organic speciesas well as primary emissionsof elementalcarbon.Secondaryorganicaerosolswill be modeledat first, followinga suggestionof Grosjean and SeinfeM[1989]. They have proposedthat the condensable material resultingfrom chemicalreactionsof organic species maybe representedby assigninga fractionof the emissionrate of a givenspeciesto be a productionrate for secondaryorganic aerosols.This is the first approachto be taken in the RPM. Pandiset al. [1992] have developedan improvedmethod for forming secondaryorganic aerosolsthat givesexplicityields; this method will be incorporatedinto subsequentversionsof RPM. Considerationof these additional species,aswell as the treatment of caseswith very low relative humidity, and the presenceof the precipitatingsolidphaserequire a muchmore completetreatmentof aerosolthermodynamics and chemistry. Cleggetal. [1992]and CleggandPitzer[1992]havepresentedan approachthat allowsthe solubilitiesof aerosolsrangingfrom aqueoussolutionsto dry fusedsaltsto be treated as functions of relative humidity.Their approachwill be adaptedfor inclusion in future versionsof the RPM. Semivolatileorganiccompounds,manyof which are toxic,can existin either gaseousor particulateform [Pankow,1987].We alsoplan to includeprovisionsfor treatment of this type of organicmaterial in the
as the cube root of the sum of the cubes of the
diameters of the coagulatingparticles. In the bimodal approachof the RPM, intramodal coagulationresultsin a particle within that mode; intermodal coagulationof a particle in the i th mode with one in the j th mode alwaysresults in a particle in the jth mode. That is, there is a transfer of mass concentrationfrom the smaller to the larger mode accompanied by a decreasein particlenumberin the smallermode,but no increase in particle number occurs in the larger mode. Intramodal coagulationis representedas follows.
0• = 5 -
•'•:•= 5 -
(D2+ D23)a/313(D D2)n,(DOn,(D2) dD•dD2 1,
D•I3(D•, D2)n,(DOn,(D2)dD• dD2
(A1)
D2)n;(DOn;(D2) dD•dD2 I (D2+D2•)a/313(D•, D•I3(D•,D2)n;(DOn;(D2) dD• dD2
(A2)
Intermodal coagulationis representedby
RPM.
The work presented here concentrateson anthropogenic aerosols.Soil-derived and marine materials are also major contributorsto atmosphericaerosols.Some important pollution problemsare associated with the resuspension of material that has been dry-depositedand adsorbedonto soil particles. As mentionedin the introduction,Westphalet al. [1988] presented model results for the mobilization and transport of Saharandust. Our approachwill model the soil-derivedand marine aerosolsby adding a third mode for theselarger particles. Sedimentation
Appendix: Aerosol Dynamics Equations
effects then must be addressed because of
the larger particle sizes.Resultsof simulationsincludingthese improvementswill be reportedin future contributions. Interaction of aerosol particles with cloud droplets is another important processthat must be included.Chaumerliac [1984] and Chaumerliacet al. [1986]presenteda methodology for this interaction.We have adopted their approach,which uses a two-stepprocesssuggestedby Slinn [1974] in which
(•0 = -
•q, =
D•I3(D•,Dx)n•(DOn•(D2) dD•dD2
(A3)
(D• + D2•)•'/313(D•, D2)n•(D•)n,(D2) dD•dD2
-
D•I3(D•,D2)n•(D1)n,(D2) dD• dD2
(A4)
where/3(D•, D2) is the Browniancoagulationkernel [Friedlander, 1977;SeinfeM,1986]. Whitbyet al. [1991] showhow theseintegralscan be simplified by examiningsizeregimesexpressedin termsof the Knudsen number Kn, which is defined as the ratio of the mean free
BINKOWSKI AND SHANKAR: REGIONAL
PARTICULATE
MODEL
26,205
path of air to the radiusof the particle.At standardconditions, the harmonicmean approachand the familiar Fuchs-Sutugin method is of the order of 15%. the mean free path for air is about 0.065 Value of Kn
Size Regime A2.
10 < Kn 1 < Kn
free molecule(fm)
_< 10
transition
0.1 < Kn _< 1
near continuum(nc)
Kn
continuum
_< 0.1
For Knudsennumbersgreaterthan 10 the particlesmay be thoughtof as free molecules,and the physicalpicture of the kinetic theory of gasesis relevant.For Knudsennumbersless than e.1, the particlesmay be visualizedasbeing suspendedin a fluid. For Knudsennumbersbetween1 and le (the transition regime),variousempiricalcorrections are availableto describe the behavior of particles [Friedlander,1977; SeinfeM, 1986]. Whitby et al. give complete details on these correctionsand show specializedequations developed for the present approach.They also showthat the coagulationkernel may be representedby combiningtwo asymptoticforms, the free mo-
Growth
Aerosol particlesgrowby the additionof new material onto existingparticles.Neglectingthe Kelvin effect,the growthrates for the kth moment of the ith and jth modes of the aerosol distributionare givenby [Whitbyet al., 1991] 2k
Gk, = -- xItrlk, 2k
Gas= --•rla
lecularform•fm andthe nearcontinuum form/3"c,givenby
•fm __W/
D-• +•22 (D1 +32)2 (AS)where •r
/3he= +32)• +•22 --+ 1)] 3t•/ • ' D•2 •222 (2kTI(D i +24921 (1
givenby •,
Ca•, - fm Caq, •nc Ca•, •nc respectively. The free-
molecularform (A5) requiressome algebraicmanipulation before integrationand table lookup for a constant(of the order of 1) relevantto intermodaland intramodalcoagulation to achievethis simplification.•itby et al. [1991] then use a deviceproposedby Pratsinis[1988] that expresses the coagulation coefficientin termsof the harmonicmean betweenonly the free-molecularand near-continuumexpressions. The •o intermodalterms thus are givenby (6a) and (6b)
s
(A8)
lki---
D•-3½(D)n,(D) dD
(A9)
I•j =
Dk-3½(D)ni(D)dD
(Ale)
is a size-independent componentof the growthlaw
given by
mwPs(Sv- 1) plRT
(A6) where X is the mean free path of air (centimeters).The common way of treating coagulationalsowould include a coagulation kernel appropriate to the transition regime and a numerical quadrature for all three regimes, as done by Giorgi [1986], for example. Numerical quadraturesare, however, computationallyintensive.•itby et al. [1991] follow a different approach.They show that the free-molecularand nearcontinuumcoagulationintegralsmaybe evaluatedanalytically. For free-molecularcoagulationand near-continuumcoagulation, the integralscorresponding to (A1) through (A4) are
(A7)
and ½(D) is the size-dependentcomponentand has two asymptotic forms for free-molecular and near-continuum size rangesgiven by
(All) ½,c= 2rrDvD
(A12)
Integrating(All) and (A12) and applyingthe sameaveraging conceptdevelopedfor particlecoagulation,the integrals(A9) and (Ale) are givenby
(A13) ?fm?nc \ ?fm. ?nc/ (A14) ?fm?nc 5 •ki •ki • ?fm •_ ?nc/ -- Xkt /
Iki• iki•
Xkt
I• • ]• • l}• =
'U
4
-- 'U
/
M(a-1)i (A15)
fm•nc ko • kij
l•,c= 2•'Dvi(/c_2) i
fm•nc kji • kji
(A16)
while both intramodaltermsare of the form (equation(6c)) fm•nc
Pratsinis[1988]showedthat thistypeof averagingapproachfor particlegrowthis a very good approximationfor the transition regime.Values for the vapor diffusivity(0.08) and accommo•itby et al. [1991] arguethat in general,this methodis within dationcoefficient(0.05) are takenfrom VanDingenenandRaes 20% of the methodthat includesthe transitionregime,and, for [1991]. typicalatmospheric valuesof •g• and • of 1.5 or greater If the growthprocessesare fast comparedwith the genera[•itby, 1978], the differenceis about 10%. Pratsinis[1988] tion of condensablevapor, a steadystate developswhere the alsoshowsthat in the transitionregime,the differencebe•een volumegrowthrate of the particlesis equal to the production kll •
C kll•
kll
• fm • nc Call + Call
26,206
BINKOWSKI AND SHANKAR: REGIONAL
rate of the vapor. The total growthrate of particlethird moment is the sum of the growthrate of the two modes:
G3 = G3i+ G3j
PARTICULATE
MODEL
KW alsogive an empiricalequationwhichwasfit by Wexleret al. [1994]to the nucleationratesof Jaecker-Voirol and Mirabel [1989]for a criticalconcentrationof sulfuricacid Ccrit(microgramsper cubicmeter) abovewhichnewparticlesare formed,
Thistotalmustthenbe equalto M3, therateof production of
Ccrit= 0.16 exp (0.1T-
third moment from condensablevapor:
3.5rh- 27.7)
(A24)
where T (kelvins)is temperature,and rh is fractionalrelative humidity[0, 1]. Thus when Cssis greaterthan Ccrit, new parThe fractionof the materialinjectedinto eachmodeis givenby
ticles are formed from the excess and with the rest of the mass
the coetficients l•i and1•i'
being condensedon the existing particles. As mentioned above,this followsfrom the ideas set forth by Middletonand Kiang[1978].KW usea sectionalparadigmand assignall of the massof newlyformed particlesto the smallestsizebin. In the modalparadigm,we distributethesenewlyformedparticlesin the i mode usingthe samemodal parametersas for initializa-
G3i +G3j] =(]3i + •J= G3, + G3j/= I73i+•3 j
tionandemissions; thatis,D g andfighavevaluesof 0.01/am
Substituting (A13) and (A14) into (A7) and (A8), recognizing and 1.6, respectively. that the fractionalgrowthratesfor eachmodeare the product
of (A17)and(A18)with/15/3, andnotingthatthegrowthrate A4. Dry Deposition for anymomentcanbe expressed in termsof the third-moment Deposition for monodisperseaerosolsis governedby two growth rate, we then can write the final expressions for the key quantities,the Brownianparticle diffusivity condensationalgrowth terms for any moment as (equations (7a) and (7b)
Dp= 3yrVpair D Cc
(A25)
and the gravitationalsettlingvelocity
vc l•vv (pPai2) D Cc
(A26)
Note that •r hascancelledout in (A17) and (A18) aswell as where the linearizedslip correctionis givenby: in (7a) and (7b). The rate of increaseof M3 by vaporcondenCc = 1.0 + 1.246(2MD) (A27) sation, M3, isobtained fromthevaporcondensation rate(mass per unit time) as follows.Recall that total aerosolvolume For a polydisperseaerosol,we averagethesequantitiesover concentrationis given by
thekth moment(Mk) of thesizedistribution n(dp)asfollows
V = (,r/6) M3
(A19)
[cf. Kramm et al., 1992]:
Dividingthe vapor condensation rate by (rr/6) timesthe density of the condensedvapor yieldsthe rate of increaseof m 3 due to vapor condensation(equation(8)). A3.
& =•
XD•'n(ln D)dInD
(A28)
whereX = Dp or vo. Substituting forDp andvo, performing
Nucleation
the integrationsassuminga lognormalsize distribution,sim-
Kerminenand Wexler[1994](hereinafterreferredto asKW) havedescribeda parameterizationof nucleationwhichwe have adapted to our modelingparadigm.They start with the rate equationfor the productionof sulfuricacid concentrationC (microgramsper cubicmeter)
dC/dt = P - Crg•
(A20)
whereP is the rate of gasphaseproductionof sulfuricacidand the timescaler• (seconds)for condensationon the existing particlesis givenby
rg•= I•,,+ I•,•
tion can be solved as
(A22)
where the steadystate concentrationis givenby
Css= Pr•
/)pk =Opg{ exp ((--2•+ 1)In 2Crg) +1.246KngeXp((-4k+4) ln2crg)} (A29) 2
with
Dpg = 37rPPairOg /
(A21)
KW arguethat r• is short enoughthat both r• and P can be held constantover somesmalltime intervaland the rate equa-
C(t) = Css- [Css- Co]exp(-trg •)
plifyingthealgebra, andlettingKng = 2A/Dg,we get
(A23)
(A30)
for the polydispersediffusivity,and
•+4)In 20'g) 0Ok =•Og{ exp ((4k + 1.246Kngexp -2 1) (2k+ ln2 trg) } with
(A31)
BINKOWSKI AND SHANKAR: REGIONAL
•
for the polydispersesettlingvelocity.Note that for a monodis-
the diffusivityand settlingvelocityincludingthe slip corrections.The depositionvelocityfor the kth moment of a polydisperseaerosolis then givenby
V/bp•, andSty,= (u,2/gv)bak, respectively. Theformforthe surfacelayer resistanceis well known [e.g., Seinfeld,1986; Slinn, 1982]exceptfor the facter involvingthe convectivevelocityscale,w,, an empiricalcorrectionobtainedby Weselyet al. [1985]who approximatedthe factor involvingthe Schmidt and Stokesnumbersby a constantof 0.002. When treating multimodal aerosol distributions,we must considerthe valuesof bd• describedabove as determinedfor eachmode.Assumingthat particledensityis not a functionof size and is the samefor each mode,we can define the depositionvelocityfor total particlemomentas a weightedaverage over both modes,and we have equation(13)
mkibd•i+ m•jbd•j A4.
Mki+
k=0,3
Particlenumberconcentration(k = 0) is predictedusing (5). New particleproductionratesare representedby E oi and
Eoi. Thisincludes emissions for bothmodesandnucleation onlyin the i mode.The speciesmass(e.g., sulfateand ammonia) is predictedusing(1). Total particlevolumeis constructed usingthe sulfateand ammonium(derivedfrom the ammonia), water, any other additionalspecies,and appropriatedensities. The number concentration, diameters, and standard deviations the third moment
the free-molecular sizerange,/am k cm-3 s-•.
Ccitt critical concentrationfor productionof new
particles(seeappendix for details),/xgm-3. Css steadystate concentrationfor condensationon
existingparticles(seeappendixfor details), m
•',
fraction
in each mode. The total
particlevolumethen is convertedto third momentby dividing by (z'/6) and the third and sixthmomentsconstructed for each mode.Equations(5) are solvedwithoutthe transporttermsfor k = 3 and k = 6. New diameters and standard deviations then
can be calculatedand the cycle advanced.If the standard deviationsare fixed, the sixth moments are not calculated.
AS. Computational Details
The advectionalgorithmsare identicalto RADM (i.e., the Smolarkiewicz [1984]scheme).The advectiontime stepin this implementationis 900 s. Calculationsdone by Whitbyet al. [1991]confirmthat the aerosoldynamicsalgorithmsare robust enoughat this time step.We recognizethat nucleationbursts happen at short timescales;but the smoothedhourly plots givenby Easterand Peters[1994]suggestthat our parameterization of nucleationis compatiblewith this time step.
.
the near-continuum sizerange,/am • cm-3 sD
particle diameter,/am.
D g geometric meanparticlediameterfor lognormal size distribution,/am.
Dv vapordiffusivity, cm2 s-•.
Dp particle diffusivity, cm2 s-•. Dw• wet deposition lossrateof species l, ppms-•. E• emissions ratefor species l, ppms-•. E•i, E• emissions ratesfor momentk of modesi andj, respectively,/xm • cm-3 s-• Gk•, G• meancondensational growthratesfor moment k of modesi andj, respectively,/am • cm-3 s-•.
]•, ]•i integrals which contribute tomean condensational growthrates (see appendixfor
details),/am k cm-3 s-•. L•
lossrate of speciesI due to gasphasechemical
reaction,s- •. LWC
liquid water contentof aerosolparticles, --3
.
M• kth momentof the numberdistribution,/am cm
--3
.
M•, M•
kth momentof the numberdistribution for modesi andj, respectively,/am • cm-3. 3;/k totalrate of changeof thekth momentof the numberdistribution,/am • cm-3 s-•. mw molecular weight,cms-•.
n(ln D)
distributionfunctionfor the number
concentration of aerosolparticles, cm-3 /am-•. N
total numberconcentrationof aerosolparticles, cm
--3
.
/•
timerateof changeof the totalnumber concentrations of aerosolparticles, cm3 s-•.
p•
saturationvapor pressureof condensingspecies, atm.
P* Psfc- Ptop,mbar. Psfc surfacepressure,mbar.
Prop pressure at modeltop (100mbar),mbar. P• productionrate of speciesI due to gas-phase
chemical reaction,ppms-•. R• ratio of molecularweight of speciesI to molecularweight of air.
R gasconstant, J øK-• mol-•. S•
saturationratio of condensingspecies.
V horizontal windvelocity,m s-•. Vd• particle depositionvelocityfor kth moment, cm S
Notation
--3
O•,t, intermodal andintramodal coagulation ratesfor
m
Prediction Cycle
determine
C•i•,.•f•jj. intramodal rate,/am •cm -3rates s-•.for intermodalcoagulation andintramodal coagulation
Cki•,
(A34)
where the Schmidtand Stokesnumbersare given by Sck =
intermodal coagulation rate,/am • cm-3 s-•.
"fm
(A33)
whichis a generalizationof a form obtainedindependentlyby Slinnand Slinn [1980]andPleimet al. [1984].The surfacelayer resistanceis givenby
Vd• =
--1
.
vo particlesettling velocity, cms-•.
Awl aqueous production rateof species l, ppms-•. •
26,207
totalrateof change of concentration of species l, ppms-•.
Ckii,C•
persedistribution (trg= 1.0),werecover thecorrectformsfor
Pdk = (Sc[ 2/3 + 10-3/stk) 1+0.24 •2,2j u,
MODEL
C• molar mixingratio of speciesl, ppm.
Vcg = 1• Pair Dg
•dk= (ra+ •dk+ ra•d/•Gk) -1 + •G/•
PARTICULATE
a
accommodation
coefficient.
kinetic velocityof vapor molecules,equal to
X mean free path of air, cm.
(8RT/•mw)1/2.
• kinematic viscosity of air, cm2 s-•.
26,208
BINKOWSKI
AND SHANKAR: REGIONAL
p• densityof species l, g cm-3.
pp density ofparticles, g cm-3. Pair densityof air, g cm-3. cr (P - Ptop)/P*. • timerateof change of o-,s-s. o-g geometric standard deviation of lognormal size distribution.
½(D) size-dependent portionof growthlaw,m3 s-•. •T
size-independentportion of growth law.
fli, fl i partitioncoefficients for condensational growth of i andj modes(see appendixfor details).
PARTICULATE
MODEL
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(ReceivedOctober12, 1993;revisedApril 14, 1995; acceptedJune 29, 1995.)
