NASA Technical Reports Server (NTRS) 20130014804: A Fast and Efficient Version of the TwO-Moment Aerosol Sectional (TOMAS) Global Aerosol Microphysics Model

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A Fast and Efficient Version of the TwO-Moment
Aerosol Sectional (TOMAS) Global Aerosol Microphysics
Model
Y. H. Lee a & P. J. Adams a b
a NASA Goddard Institute for Space Studies and Center for Climate Systems Research,
Columbia University, New York, New York, USA
b Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh,
Pennsylvania, USA
Accepted author version posted online: 29 Nov 2011.Version of record first published: 19 Jan
2012.
To cite this article: Y. H. Lee & P. J. Adams (2012): A Fast and Efficient Version of the TwO-Moment Aerosol Sectional (TOMAS)
Global Aerosol Microphysics Model, Aerosol Science and Technology, 46:6, 678-689
To link to this article: http://dx.doi.org/10.1080/02786826.2011.643259
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AerosolScienceandTechnology,46:678–689,2012
Copyright(cid:2)C AmericanAssociationforAerosolResearch
ISSN:0278-6826print/1521-7388online
DOI:10.1080/02786826.2011.643259
A Fast and Efficient Version of the TwO-Moment Aerosol
Sectional (TOMAS) Global Aerosol Microphysics Model
Y. H.Lee1andP. J.Adams1,2
1NASAGoddardInstituteforSpaceStudiesandCenterforClimateSystemsResearch,Columbia
University,NewYork,NewYork,USA
2DepartmentofEngineeringandPublicPolicy,CarnegieMellonUniversity,Pittsburgh,Pennsylvania,
USA
3
1
0
2
ril
p
A [Supplementarymaterialsareavailableforthisarticle.Goto
16 Thisstudydevelopsmorecomputationallyefficientversionsof thepublisher’sonlineeditionofAerosolScienceandTechnology
7 the TwO-Moment Aerosol Sectional (TOMAS) microphysics al- toviewthefreesupplementaryfiles.]
4
4: gorithms,collectivelycalled“FastTOMAS.”Severalmethodsfor
1
] at snpuemedbienrgoufpsitzheesaelcgtoiornitshmwawseardeoapttteedm.pFtaesdt,TbOutMoAnlSymreoddueclisn,gcothue- 1. INTRODUCTION
es pled to the GISS GCM II-prime, require a new coagulation al- Changes in aerosols that act as cloud condensation nuclei
di gorithmwithlessrestrictivesizeresolutionassumptionsbutonly (CCN)sincetheIndustrialRevolutionarebelievedtoenhance
u
St minorchangesinotherprocesses.FastTOMASmodelshavebeen cloud reflectivity, known as the cloud albedo effect (Twomey
e evaluated in a box model against analytical solutions of coagu-
c 1974), and to modify precipitation efficiency and cloud distri-
pa lation and condensation and in a 3-D model against the original
S TOMAS (TOMAS-30) model. Condensation and coagulation in bution,knownasthecloudlifetimeeffect(Albrecht1989).The
or the Fast TOMAS models agree well with the analytical solution effects of aerosols on clouds are among the most uncertain of
f
e butshowslightlymorebiasthantheTOMAS-30boxmodel.Inthe anthropogenic climate forcings (Solomon et al. 2007). These
stitut 3p-rDocmesosd(eil.,e.e,rreomrisssrieosnusl,tinclgoufrdomprdoeccersesainsged/wseiztedreepsoosluittiioonn,imniecarcoh- aerosol “indirect effects” are not easily estimated from obser-
n vations because of natural variability in cloud properties and
d I physics)arequantifiedinaseriesofmodelsensitivitysimulations. thelackofobservationsofthepre-industrialatmosphere.Thus
r Errors resulting from lower size resolution in condensation and
a
d coagulation,definedasthemicrophysicserror,affectnumberand estimations of the impacts of aerosols on global radiative flux
d
o massconcentrationsbyonlyafewpercent.Themicrophysicserror changehavebeenmainlybasedoncomputermodeling.
G
A in CN70/CN100 (number concentrations of particles larger than Recently,agrowingnumberofglobalaerosolmicrophysics
S 70/100nmdiameter),proxiesforcloudcondensationnuclei,range
A models have been developed to improve our understanding of
from–5%to5%inmostregions.Thelargesterrorsareassociated
N
aerosol–cloud interactions and specifically the processes that
[ withdecreasingthesizeresolutioninthecloudprocessing/wetde-
by positioncalculations,definedascloud-processingerror,andrange controlCCNconcentrations(AdamsandSeinfeld2002;Lauer
d from –20% to 15% in most regions for CN70/CN100 concentra- etal.2005;Spracklenetal.2005;Stieretal.2005;Pierceand
e
ad tions.Overall,theFastTOMASmodelsincreasethecomputational Adams 2006; Pierce et al. 2007; Bauer et al. 2008; Trivitaya-
nlo speedby2to3timeswithonlysmallnumericalerrorsstemming nurak et al. 2008; Lee et al. 2009; Makkonen et al. 2009; Yu
w from condensation and coagulation calculations when compared
Do toTOMAS-30.ThefasterversionsoftheTOMASmodelallowfor and Luo 2009). Because CCN behavior depends strongly on
thelonger,multi-yearsimulationsrequiredtoassessaerosoleffects particle size, these models have included specific treatment of
oncloudlifetimeandprecipitation. aerosolmicrophysicalprocesses.Thesemodelssolvetheaerosol
generaldynamicequation(GDE)thatgovernshowtheaerosol
sizedistributionevolvesovertimeasaresultofmicrophysical
processessuchasnucleation,condensation/evaporation,andco-
agulation.AccurateandflexiblealgorithmsforsolvingtheGDE
Received26July2011;accepted26October2011. areespeciallynecessarytoobtainprecisenumberandmassdis-
ThisstudywassupportedbytheEnvironmentalProtectionAgency tributions of aerosol particles, although model performance is
(EPASTARAward83337401). mostly limited by uncertainties in key inputs. In particular, it
AddresscorrespondencetoY.H.Lee,NASAGoddardInstitutefor
appearsnecessarytotreatthemicrophysicsofultrafineparticles
Space Studies and Center for Climate Systems Research, Columbia
indetailsincemanyCCNresultfromthegrowthofthesepar-
University, 2880 Broadway, New York, NY 10025, USA. E-mail:
[email protected] ticles to CCN sizes (Pierce et al. 2007; Spracklen et al. 2008;
678
FASTANDEFFICIENTTOMASMODELS 679
Merikanto et al. 2009; Chen et al. 2010). Thus it is important TheTwO-MomentAerosolSectional(TOMAS)aerosolmi-
for these models to have sufficient size resolution in the size crophysicsmodelhasbeenimplementedintotheclimatemodel
range of particles that contribute the most CCN (Zhang et al. of Goddard Institute for Space Studies General Circulation
2002; Korhonen et al. 2005). For the coarse mode (1 μm < Model II-prime (GISS GCM II-prime) referred as “GISS-
particlediameter<10μm),detailedmicrophysicscalculations TOMAS”model(LeeandAdams2010),ortheGEOS-CHEM
maynotbenecessarybecausetheirgrowthratesareslow,and model(Trivitayanuraketal.2008),andtheregionalmodelPM-
theircontributiontoCCNnumberconcentrationsarenegligible CAMx,referredasPMCAMx-UF(Jungetal.2010).Modules
(Heintzenberg1989;Raesetal.2000). for each of the major aerosol species have been developed for
In general, accurate and flexible algorithms for solving the the GISS GCM, and the GISS-TOMAS model (i.e., TOMAS-
GDE impose a high computational burden, and this is an im- 30 model in the paper) have been evaluated with ground-level
portant issue in large-scale aerosol transport models that must measurements such as number and mass concentrations, de-
balancepredictionaccuracyversusfastercomputertime.Aspe- position fluxes, and remote sensing observations (Adams and
cial challenge is to simulate cloud lifetime effects. Because Seinfeld2002;PierceandAdams2006;Pierceetal.2007;Lee
3 thesesimulationsperturbthemeteorologicalfieldsoftheglobal etal.2009;LeeandAdams2010).Coagulationandcondensa-
01 model, long (multi-year) simulations are required to separate tionintheoriginalTOMASmodelhavebeenevaluatedagainst
2
ril the aerosol effect (signal) from chaotic meteorological vari- analyticalsolutionsandhaveshownexcellentagreement(Jung
p ability (noise). Methods for solving the GDE differ primar- etal.2010).ThisfeaturemakestheTOMASmodelanexcellent
A
6 ily in how they represent the aerosol size distribution and can toolfortheaerosolindirecteffectstudy.However,theTOMAS
1
7 becategorizedintomoment,modal,andsectionalapproaches. modeldominatesthecomputationaltimeoftheGISS-TOMAS
4
4: Moments-based approaches track lower-order radial moments modelthatismostlyduetothemicrophysicsandtracertransport.
at 1 of the size distribution, and modal approaches use analytical Thegoalofthisworkistodevelopmorecomputationallyef-
] functions(e.g.,lognormaldistributions)thatrepresentthesev- ficientversionsoftheTOMASmodel(hereafter,FastTOMAS)
s
die eralmodesoftheparticlepopulation.Sectionalapproachesrep- whilestillmaintainingacceptableaccuracy.Section2includes
u resent a size distribution by predicting the amount of aerosols theoriginalTOMASmodeldescription,andSection3explains
St
e inseveralsizesectionsor“bins.”Single-momentsectionalap- the methods used to develop the Fast TOMAS models. Sec-
c
a proachestypicallytrackeitheraerosolnumberormassineach tion 4 shows results of box model evaluation of Fast TOMAS
p
S
r bin, while two-moment sectional approaches explicitly track modelsagainstanalyticalsolutionsofcoagulationandconden-
o
f both aerosol number (i.e., zeroth moment) and mass (i.e., first sation. Section 5 evaluates Fast TOMAS against the original
e
ut moment) in each size section. Two-moment sectional method TOMASmodelinthecontextofaglobal,3-Dmodelandana-
stit can conserve both number and mass very accurately (Tzivion lyzessourcesoferrorinthiscomparison.Section6isasummary
n
I etal.1987;Tzivionetal.2001;AdamsandSeinfeld2002;Jung anddiscussionofthisstudy.
d
ar etal.2006),whereassingle-momentsectionalapproachesmay
d
d result in less accurate aerosol number information than two-
o
G momentsectionalmethod(HarringtonandKreidenweis1998). 2. ORIGINALTOMASMODELDESCRIPTION
A
S The modal and the moments-based approaches are generally Basedonearlieralgorithmsfortreatingcloudmicrophysics
A
morecomputationallyefficientbutlessaccuratethansectional (Tzivion et al. 1987; 1989), the TOMAS global microphysics
N
y [ approaches.Forexample,thesectionalapproachisshowntobe modelwasadaptedforaerosolsbyAdamsandSeinfeld(2002)
d b moreaccurateandflexiblewhendealingwithabrupttransitions andwasincorporatedintotheGISSGCMII-prime.TheGISS
de in a size distribution occurring during aerosol activation pro- GCM II-prime has horizontal grid dimensions of 4◦ latitude
oa cesses(Zhangetal.1999).Thus,eventhoughtheyarecomputa- by 5◦ longitude and vertical grid dimensions of 9 vertical lay-
nl
w tionallyexpensiveinaglobalmodel,theiraccuracyandflexibil- erscoveringthetroposphereandthestratospheretothe10-hPa
o
D ityhasfoundseveralapplicationsin3-dimensional,global-scale level(Hansenetal.1983).AdamsandSeinfeld(2002)providea
models (Jacobson 2001; Adams and Seinfeld 2002; Spracklen detaileddescriptionoftheTOMASmodel,andLeeandAdams
et al. 2005; Trivitayanurak et al. 2008; Lee et al. 2009). How- (2010)providemostupdateddescriptionofitsimplementation
ever,theircomputationalrequirementslimittheiruse,especially intotheGISSGCM.Here,itsimportantfeaturesarebrieflysum-
for multi-year simulations that are generally required to study marized.The“TwO-Moment”referstothetwomomentsofthe
aerosolindirecteffects.AsaglobalCCNmodel,itisimportant aerosolsizedistributiontrackedforeachsizebin,totalaerosol
toachieveacomputationalefficiencyaswellasanaccuratepre- number, and mass concentrations for each aerosol species, to
diction.Avarietyoftechniquesareused(moment,modal,and predicttheaerosolnumberandmasssizedistributions(Tzivion
sectional) for a global CCN model, but little systematic work et al. 1987; 1989) and, therefore, represents a highly accurate
has been done to evaluate accuracy and to compare compu- andflexibledescriptionofaerosolmicrophysics.
tational speed of different configurations. This work evaluates The original model has thirty size sections (hereafter,
theaccuracyofdifferentsectionalmodelconfigurationsforthe TOMAS-30)withthelowerboundaryofthesmallestsizebinbe-
specificpurposeofpredictingaerosolnumberdistributionsand ing10−21kgdrymassperparticle,andeachsuccessiveboundary
CCNconcentrationsonaglobalscale. has twice the mass of the previous boundary (so-called “mass
680 Y.H.LEEANDP.J.ADAMS
doubling”). For typical aerosol densities, the TOMAS-30 size 0.2%and1.0%,respectively.Forin-cloudscavenging,modified
distribution therefore ranges approximately from 10 nm to 10 Ko¨hler theory is used to determine the activation diameter for
μm in dry diameter. The model tracks 9 quantities for each thecriticalsupersaturation,andparticleslargerthantheactiva-
size bin: total number of aerosol particles, sulfate mass, sea- tiondiameterareactivatedandsubjecttonucleationscavenging
salt mass, mass of pure (externally mixed) elemental carbon, (Lee et al. 2009). Note that in-cloud scavenging is applied to
massofinternallymixedelementalcarbon,massofhydropho- internally mixed elemental carbon but not to externally mixed
bic organic matter, mass of hydrophilic organic matter, min- elementalcarbon.Whentheactivationdiameterisintermediate
eral dust mass, and aerosol water mass. The model includes betweenthesizeboundaries,thefractionofparticlesactivatedin
aerosol microphysics processes, such as condensation of sul- thebinisdeterminedbylinearinterpolationwithintheactivat-
furicacid,coagulation,nucleationandin-cloudoxidation,and ingsizeboundaries(i.e.,dryaerosolmass).Foraerosolactiva-
size-resolvedemissionsanddeposition.Sulfuricacidconcentra- tion,allaerosolsaretreatedasinternallymixedexceptforpure
tionsusedforthenucleationandcondensationratesaresolved elemental carbon. Dry deposition uses the resistance-in-series
simultaneouslywiththepseudo-steadystateassumption(Pierce approach that treats a size-dependent gravitational settling of
3 andAdams2009a),andthegrowthofnucleatedparticlesupto particles and a size-dependent resistance in the quasi-laminar
01 thefirstsizebin,adiameterof10nm,istakenintoaccountusing sublayer.Aerodynamicresistancesarecalculatedasafunction
2
ril the parameterization of Kerminen et al. (2004). Details of the ofGCMsurfacemomentumandheatfluxes.Nosurfaceresis-
p TOMASmodelforsulfate(AdamsandSeinfeld2002),sea-salt tanceisassumedforaerosolspecies.
A
6 (PierceandAdams2006),carbonaceousaerosols(Pierceetal.
1
7 2007), and mineral dust (Lee et al. 2009) have been described
4
4: elsewhere,butabriefdescriptionofaerosolemissionusedfor 3. FASTTOMAS
at 1 this work is provided here. Primary sulfate is assumed to be The computational burden of GISS-TOMAS mostly results
] 1% of anthropogenic sulfur emissions and to be emitted in 2 fromthe2-momentsectionalapproachthatusesthirtysizebins
s
die modes;15%ofthemasstohavealognormaldistributionwith (e.g.,about5.6daysfora1-monthsimulationwithTOMAS-30
Stu a number median diameter (NMD) of 10 nm and a geometric usinga250MHzsingleprocessorofanSGIOrigin2000).To
e standarddeviation(GSD)of1.6and85%ofthemasstohavea speed computations, the number of size bins is reduced with
c
a lognormal distributionwitha NMDof 70 nm and a GSD of 2 thefollowingmannerasshowninTable1.First,theTOMAS-
p
S
r (AdamsandSeinfeld2002).Emissionsfromfossilfuel,biofuel, 15 model is developed by merging each 2 adjacent bins in the
o
f andbiomassburningarebasedonBondetal.(2004),and1.8is originalTOMASmodel,therebydecreasingthenumberofsize
e
ut usedastheconversionoforganiccarbonmasstoorganicmatter binstofifteen.Second,wetakeadvantageofthefactthatcoarse
stit (Pierceetal.2007).Thesizedistributionofbiofuelandbiomass particleshaveslowmicrophysicsanddonotcontributemuchto
n
I burning carbonaceous emission follows a lognormal distribu- CCNconcentrationsand,thus,wedecreasethesizeresolution
d
ar tionwithaNMDof100nmandaGSDof2,and,forfossilfuel, ofthecoarsemodefurtherto2binsandcallthismodelversion
d
d alognormaldistributionwithaNMDof30nmandaGSDof2 “TOMAS-12.”
o
G isassumed(Pierceetal.2007).Sea-saltemissionsarebasedon With these new size resolutions, several aerosol processes
A
S theemissionsparameterizationofClarkeetal.(2006).Notethat need to be changed: aerosol emissions, deposition, in-cloud
A
mineraldustisexcludedinthisworkbecausethedustemission scavenging, aqueous oxidation, and microphysical processes
N
y [ parameterization cannotproduce thesameemissionratewhen (condensationandcoagulation).Exceptcoagulation,mostpro-
d b reducingsizebins.Withmineraldust,itwouldbeproblematic cesses require minor changes or are straightforward to imple-
de toestimate“emissionerror”(Section5.1). ment. However, the coagulation scheme used in the original
a
o Description of wet deposition and dry deposition can be TOMAS-30 model is based on Tzivion et al. (1987), in which
nl
w found in Adams and Seinfeld (2002) and Lee et al. (2009). thestochasticcollectionequationisreducedtoasetofmoment
o
D Briefly wet deposition occurs in large-scale (stratiform) and equationsforeachsizesectionusing2moments,Nk (thetotal
convectivecloudsthatareassumedtohaveasupersaturationof number of aerosol particles in the k-th size bin) and M (the
k
TABLE 1
ConfigurationsofsizeresolutioninTOMAS-30,TOMAS-15,andTOMAS-12
Aitkenmode Accumulationmode Coarsemode
TOMASmodel (10nm<D <100nm) (100nm<D <1μm) (1μm<D <10μm)
p p p
TOMAS-30 10bins 10bins 10bins
TOMAS-15 5bins 5bins 5bins
TOMAS-12 5bins 5bins 2bins
FASTANDEFFICIENTTOMASMODELS 681
massofaerosolparticlesinthek-thsizebin),thatarepresented f −ψ (cid:2)k−1 K M N
in Equations (1) to (4) in Adams and Seinfeld (2002). These − k6xk kξ3 Kk,iMim2i − k,k3k k
equations for TOMAS-30 assume mass doubling size bound- i=1
aries,whichsimplifiesthecoagulationequationbyeliminating −ψkK M x − fk+2ψkK M m ξ
self-coagulation in a size bin, defined here as the coagulation 3 k,k k k+1 18 k,k k k
owfit2hmpaarstsicilnesthferoomrigtihnealssaizmeesesciztieonse(cTtzioivniotnoeftoarml.1a98p7a)r.tiFcoler −fk1−8xψk kKk,kMkm2kξ3 [2]
the TOMAS-15 model, a new set of equations for coagulation
rate must be obtained using mass quadrupling section bound- whereK isthecoagulationcoefficientforparticlesinthek-th
k,i
aries and are based on Tzivion et al. (1999; 2001). The basic binwithparticlesinthei-th,x isthelowerboundaryofthek-th
k
approach is quite similar to that applied to TOMAS-30, and sizebinintermsofdrymass,m istheaveragemassofparticles
k
Equations(1)and(2)showhowaerosolnumber(Nk)andmass inthek-thbin,I isthetotalnumberofsizebins,ξ isaclosure
(Mk)evolvewithtimeintheTOMAS-15model. parameterthatdependsonthebinspacing(equals1.28125for
3 themass-quadruplingusedhere),fk and(cid:4)k areparametersthat
1
0 dN (cid:2)k−2 f −ψ (cid:2)k−2 describethelinearapproximationtothenumberdistributionand
April 2 dtk =ψk−1 i=1Kk−1,iMi + k−61xk−1k−1ξ i=1Kk−1,iMimi asureffidceiefinntelyd ignenTezriavliotonaeptpally. (t1o9T9O9)M. EAqSu-a1t2ionass (w1e)llanwdit(h2)onalrye
7 16 +0.625Kk−1,k−1Nk2−1+ ψk3−1Kk−1,k−1Nk−1mk−1 msizineorresmoloudtiiofincaotifotnhse.2FsoercTtiOonMsAinSt-h1e2c,oξaresqeumalosd4e..754 for the
4
at 14: +fk−118−xk−ψ1k−1ξKk−1,k−1Nk−1m2k−1−1.125Kk,kNk2 meTthhoedscaosagAudlaatmiosnankderSneeiln,fKelkd,i,(2i0s0c2a)l.cIunlabtreidef,uosninlygBthroewsnaimane
s] (cid:2)I (cid:2)k−1 diffusion is accounted for in the coagulation kernel using the
e
di −Nk Kk,iNi −ψk Kk,iMi particle diffusivity based on the Stokes-Einstein formula, and
u
St i=k+1 i=1 the correction factor for the transition and kinetic regime is
ce f −ψ (cid:2)k−1 ψ based on Dahneke (1983). The kernel is recalculated at every
pa − k kξ K M m − kK N m gridcellandtimestepusingtheaveragehydratedparticlesizes
or S 6xk i=1 k,i i i 3 k,k k k inbinskandi.
stitute f −fk1−8xψk kξKk,kNkm2k [1] munesBtuhecoscdiedssefssofurrled.deFucicrresinat,gsainthRgeucnnougmmep-bKuetuarttotiaofnssoaizllvetiebmriwnesta,hswattretiueedrxnpienldotroheuedtcotoothabgeer-
n
dard I ddMtk =ψk−1xk(cid:2)k−2Kk−1,iMi uthlaatniothnemfiorsdtu-oler,dwerhEicuhleirsmaemthoordeaindvthaencoeridgninuamlTerOicMalAteScmhnoidqeule.
od i=1 However,useofRunge-Kuttaincreasedthecomputationalbur-
A G +fk−1+2ψk−1ξ(cid:2)k−2K M m den. This was because the Runge-Kutta method requires 4 it-
S k−1,i i i erations in a time step. The original model used an adaptive
A 6
N i=1 timestep,butcoagulationisslowenoughinmostgridboxes(in
by [ +fk−1−ψk−1ξ3(cid:2)k−2K M m2 theGISSglobalmodel)soonlyasingleiterationwasrequired
ded 6xk−1 i=1 k−1,i i i mkeornstelo,fwthheicthimise.aSfeucnocntdio,naolofopkr-euspsutraeb,letefmopretrhaetucroea,gpualrattiicolne
a K M N ψ
nlo + k−1,k−1 k−1 k−1 + k−1Kk−1,k−1Mk−1xk mass,andparticledensity,wastriedbut,unexpectedly,didnot
w 3 3 improvethemodelspeed.Otheraerosolmicrophysicalmodels
Do +fk−1+2ψk−1K M m ξ typicallyimplementalook-uptableforthecoagulationkernel
k−1,k−1 k−1 k−1
18 andfindthatitimprovescomputationalspeed.Ourmodeluses
f −ψ
+ k−1 k−1K M m2 ξ3 the correction factor based on Dahneke (1983), while a more
18xk−1 k−1,k−1 k−1 k−1 complexformbasedonFuchs(1964)ismorecommonlyused.
(cid:2)k−1 (cid:2)I Thechoiceofsimplerformforthecorrectionfactormayexplain
+N K M −M K N whythelook-uptablemethodwasnotsuccessful.
k k,i i k k,i i
i=1 i=k+1
(cid:2)k−1
−ψ x K M 4. BOXMODELEVALUATIONVERSUSANALYTICAL
k k+1 k,i i
SOLUTIONS
i=1
−fk +2ψkξ(cid:2)k−1K M m moNdeelws aTgOaiMnsAtSa-n1a5lyatincdalTsOoMlutAioSn-s1.2Cmonoddeenlssaatrieonteastneddcinoabgoux-
k,i i i
6 lation in TOMAS-12 and TOMAS-15 models as well as the
i=1
682 Y.H.LEEANDP.J.ADAMS
originalTOMAS-30areevaluatedagainstanalyticalsolutions. ference in total mass concentration among models is less than
The analytical solution for condensation (Seinfeld and Pandis 1%(notshown).Comparedtotheanalyticalsolution,TOMAS-
1998, pp. 654–655) assumes an initially lognormal size distri- 30 captures the correct location and magnitude of the peak of
butionandaconstantconcentrationgradientofthecondensing thesizedistributionasdoTOMAS-15andTOMAS-12models.
gas between the surface of particles and the bulk gas phase. However, the new models show slightly less growth after 10
The initial particle size distribution has a geometric mean di- minofcondensation(notshown),whichmeansthatthenumber
ameter of 200 nm, a geometric standard deviation of 2, and ofparticlessmallerthanthepeakofthesizedistributioninthe
the initial number concentration of 203 cm−3. The following newmodelsis∼10%higherthantheTOMAS-30model.
assumptions for condensation are used: constant pressure dif- The analytical solution for coagulation (Seinfeld and Pan-
ference,10−10atm;temperatureof298K;molecularweightof dis1998,pp.678–679)requiresasize-independentcoagulation
100gmol−1;particledensityof1.0gcm−3;particlediffusivity coefficient to solve the continuous coagulation equation. The
of0.1cm2s−1;idealgasconstantof82.06cm3atmK−1mol−1. comparison of number size distributions evolved by coagula-
Figure1ashowsthecomparisonofinitialandpredictedaerosol tion during 1 h is shown in Figure 1b. The initial particle size
3 number size distributions after 1 h of condensation. Because distributionisassumedtohaveanumber concentration of104
01 the 2-moment algorithms incorporate a conservation equation cm−3andvolumeof2.6808μm3withcoagulation kernelof5
ril 2 foraerosolnumberconcentrations,totalnumberconcentrations × 10−8cm3 s−1. The difference in total number concentration
p predictedbyallTOMASmodelsareconservedexactly.Thedif- predictedbytheTOMASmodelsandtheanalyticalsolutionis
A
6 less than 5%, and the difference in TOMAS-12 and TOMAS-
1
7 15modelsandTOMAS-30modelislessthan0.4%(formass,
4
4: 0.02%;notshown).TOMAS-30modelshowsexcellentagree-
at 1 ment to the analytical solution as shown in Jung et al. (2006).
] However,theTOMAS-15andTOMAS-12modelsshowslightly
s
die fastercoagulationalgrowth.
u Although the coagulation calculation in TOMAS-15 and
St
e TOMAS-30performreasonablywell,someaspectsofthecom-
c
a parisonareartificial.First,theinitialsizedistributionissome-
p
S
r what narrow, and it is expected that the coarse size resolution
o
f in TOMAS-15 and TOMAS-12 will show higher errors as the
e
ut widthofinitialsizedistributionisnarrower.Second,theanalyt-
stit icalsolutionrequiresaphysicallyunrealisticconstantcoagula-
n
I tioncoefficient.Therefore,thecomparisonsarerepeatedusing
d
ar as inputs lognormal distributions with number mean diameter
dd of 30 nm but varying their standard deviations (σ) from 1.2
o
G to 2.0, and 1-h coagulation is applied. Initially, total number
SA concentrationissetto105cm−3.Inthistest,onlyTOMAS-30
A
and TOMAS-15 models are compared with each other by us-
N
y [ ingsize-dependentcoagulationcoefficientbecausethenumber
d b predictionsfromTOMAS-12modelareidenticaltothosefrom
de TOMAS-15model.InFigure2,theTOMAS-15andTOMAS-
a
o 30modelspredictthesamemagnitudeandlocationforthepeaks
nl
w inthenumbersizedistributionsafter1hofcoagulationbutdif-
o
D ferentnumberconcentrationateachsizebin.Thedifferencein
totalnumberconcentrationbetweenTOMAS-30andTOMAS-
15inthe3casesismuchlessthan1%.Themaximumdifference
ofnumberconcentrationateachsizebinbetweenTOMAS-30
andTOMAS-15after1-hcoagulationisobservedforσ of1.2,
andisapproximatelyafactorof4,butithaslittlecontribution
tototalnumberconcentration.Themaximumdifferenceateach
FIG.1. EvolutionofthenumbersizedistributionpredictedbytheTOMAS-
30,TOMAS-15,andTOMAS-12boxmodels,comparedagainsttheanalytical sizebinisreducedtoapproximately50%and10%forσ =1.5
solutionsfor(a)condensationand(b)coagulationafter1h.Tofacilitateadirect and σ = 2.0, respectively. The difference in number concen-
evaluationoftheneweralgorithms,theanalyticalandTOMAS-30resultshave tration at each bin can be as large as 7%, 4%, and 1% of total
beengriddedtothecoarserresolutionofTOMAS-15.Detailsoftheinitialsize numberconcentrationforσof1.2,σof1.5,andσof2.0,respec-
distributionsandotherinputparametersareavailableinSection4.Notethat
tively.ThesetestsimplythatTOMAS-15andTOMAS-12may
theresultsfromTOMAS-15andTOMAS-12areidenticalandthusthelines
representing2modelsareoverlapped.(Colorfigureavailableonline.) introduce greater numerical error when dealing with a narrow
FASTANDEFFICIENTTOMASMODELS 683
model,theGISSGCMII-prime.FortheFastTOMASmodels
coupled with GISS GCM, all size-resolved processes must be
changedtoaccommodatelowersizeresolutionsinTOMAS-15
and TOMAS-12 models: emissions, cloud processing, deposi-
tion, as well as aerosol microphysics (i.e., condensation and
coagulation).Withalowersizeresolution,anyerrorassociated
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AS FIG.2. NumbersizedistributionspredictedbytheTOMAS-30andTOMAS-
N 15boxmodelsusingasize-dependentcoagulationkernelafter1-hcoagulation.
y [ Notethatinitialnumbersizedistributionisassumedtobelognormalwitha
b geometricmeandiameterof30nmandgeometricstandarddeviationsvaried
ed from1.2to2.0(σ=1.2fora,σ=1.5forb,andσ=2.0forc).Theinitialtotal
ad numberconcentrationis105cm−3.(Colorfigureavailableonline.)
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o sizedistribution.However,thetestconditionsusedhereare,in
D
fact,ratherextremecomparedtotheambientatmosphere,where
the narrow number size distributions (i.e., σ of 1.2) are quite
unusualinambientair.Overall,theFastTOMASmodelsshow
goodagreementagainsttheanalyticalsolutionsandTOMAS-30
modelwithlargererrorsundersomespecificconditions.
5. 3-DMODELEVALUATION
5.1. SourcesofErrorintheTOMAS-15andTOMAS-12 FIG.3. GlobaldistributionofemissionerrorofCN10,CN70,andCN100.
Emissionerrorisdefinedaserrorsresultingfromdecreasingthesizeresolution
Models
intheemissionprocessandisestimatedbycalculatingtheratioofCAD-30to
TheaccuracyoftheFastTOMASmodelshasalsobeeneval-
CAD-30–30EMIS.Notethatthevalueonthetoprightofeachfigureisaglobal
uatedagainsttheTOMAS-30modelinthecontextofaglobal averageoftheerrorsdisplayedinthemap.(Colorfigureavailableonline.)
684 Y.H.LEEANDP.J.ADAMS
TABLE 2
Descriptionofprocess-specificerrorsandsimulationsusedtoestimatetheerror
Errortype Errordescription Simulationsused
Cloudprocessing ErrorsresultingfromlowersizeresolutionusedtodetermineCCNactivation (KOH-15/KOH-30)∗
fractioninwetdepositionandin-cloudsulfuroxidation
OfflineCCN ErrorsresultingfromlowersizeresolutionusedtodetermineCCN(0.2%)based CAD-30outputmerged
onmodeloutput(e.g.,monthlyaerosolfield).Thisisofflineprocessinour into15-bin/CAD-30
model
Emission Errorsresultingfromlowersizeresolutionusedtorepresentemissionsize CAD-30/CAD-30–30EMS
distribution
Microphysics Errorsresultingfromlowersizeresolutionusedtocalculatecondensationand CAD-15/CAD-30
coagulationrates
3 Condensation Sameasmicrophysicsbutnochangeincoagulation CAD-15–30COA/CAD-30
1
0 Coagulation Sameasmicrophysicsbutnochangeincondensation CAD-15/CAD-15–30COA
2
pril ∗Notethatcloud-processingerrorisobtainedbymakingaratioofKOH-15toKOH-30andsubtractingmicrophysicserror.
A
6
1 with a size-resolved process will necessarily increase. In this explanation can be found in Lee et al. (2009). Fourth, errors
7
4 section,theoverallerrorsassociatedwithchangingthesizeres- directlyassociatedwithusinglowersizeresolutioninTOMAS-
4:
1 olution are separated into 4 process-specific errors (Table 2). 15 and TOMAS-12 to calculate condensation and coagulation
] at First,errorsresultingfromloweringthesizeresolutionofemit- ratesaredefinedasmicrophysicserror.Includedinthe“micro-
s
e tedparticlesaredefinedas“emissionerror.”Second,errorsfrom physics”errorsarefeedbackstonucleationrates.TheTOMAS
di
u reducing the size resolution used in cloud processing and wet modulesusethepseudo-steadystateapproximation(Pierceand
St
e deposition, calculated “online (during the simulations)” in the Adams2009a),whichassumesthatsourcesandsinksofsulfu-
ac model,aredefinedas“cloud-processingerror.”Third,errorsin ricacidvaporareapproximatelyinbalance.Changesinmodel
p
S CCNconcentrationsat0.2%supersaturation(CCN(0.2%))con- size resolution necessarily affect the condensational sink and
r
o centrationsresultingfromlowersizeresolutioninCCNcalcula- sulfuric acid concentrations, causing differences in nucleation
f
ute tionisdefinedas“offlineCCNerror.”AlthoughCCNconcentra- ratesaswellasthegrowthofnucleatedparticlesuptothefirst
stit tionsarecalculatedduringthemodelsimulationsforpurposes sizebin.
In of wet deposition, these are not saved as output. Therefore, Lastly,modelsizeresolutionwillaffectdrydepositionrates
d
r CCN(0.2%) concentrations in TOMAS models are calculated and below-cloud scavenging rates because these processes are
a
dd afterthemodelsimulationsarecompletebasedonmonthlyav- size-resolvedasexplainedinAdamsandSeinfeld(2002).Dry
o
G erageaerosolsizeandcompositiondistributions.Therefore,this depositionisimportantforcoarsemodeparticles,andFigure4
A “offline” CCN error is separated from cloud-processing error, showsanoticeablechangeinsea-saltmassfromTOMAS-15to
S
A eventhoughbothhavesimilarsources.Itisimportanttomen- TOMAS-12 (Section 5.2). Aerosol number concentrations are
N
[ tion that the activation process required for cloud-processing, notstronglyaffectedbecausedrydepositionratesareslowfor
y
b wetdeposition,andofflineCCNcalculationisbasedonmodified the accumulation mode particles that contribute most to CCN
d
e Ko¨hler theory that is explained in Section 2 but more detailed number.Similarly,errorsinbelow-cloudscavengingratesfrom
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TABLE 3
Descriptionsofsimulationsusedinthisstudy
Simulationname Condensation Coagulation Emission Cloudprocessing/Wetdeposition
KOH-30 30bins 30bins 15bins KOH
KOH-15 15bins 15bins 15bins KOH
CAD-30 30bins 30bins 15bins CAD
CAD-15 15bins 15bins 15bins CAD
CAD-12 12bins 12bins 12bins CAD
CAD-30–30EMS 30bins 30bins 30bins CAD
CAD-15–30COA 15bins 30bins 15bins CAD
Note.KOHandCADrefertoKo¨hlertheoryandconstantactivationdiameter,respectively.
FASTANDEFFICIENTTOMASMODELS 685
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S FIG.4. Globaldistributionofnumberconcentration(CN10)andmassconcentrationsforsulfate,sea-salt,andorganicmatter(showninthe1stcolumn)and
A
theirmicrophysicserrors(shownin2ndand3rdcolumns)inthelowermostverticallayer.Microphysicserrorisdefinedhereaserrorsresultingfromlowersize
N
[ resolutionusedtocalculatecoagulationandcondensationratesandisestimatedbymakingaratioofCAD-15toCAD-30(andCAD-12toCAD-30).Notethatthe
y
b upperlimitonthecolorbarisdifferentfromthoseinotherfiguresbecausethemaximumerrorinthisfigure(Figure4)exceedsthatlimitandthevalueonthetop
d rightofeachfigurein2ndand3rdcolumnisaglobalaverageoftheerrorsdisplayedinthemap.(Colorfigureavailableonline.)
e
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o a lower size resolution are expected to have little impact on 30–30EMS)useemissioninventorieswithfifteenbinsthatgive
D
CCN particles because this is not efficient to remove particles the same total number and aerosol mass as the original thirty
inaccumulationmode. emissioninventories.Toassesstheeffectofusingcoarseremis-
Various simulation scenarios used to isolate these errors in sionsinventories,CAD-30–30EMSusestheoriginalthirty-bin
thispaperaresummarizedinTable3.Thesimulationsarenamed emissionsinventories.Toseparateerrorsincondensationrates
accordingtowhatsizeresolutionisusedforvariousprocesses fromcoagulationrates,theCAD-15–30COAusesthirty-binco-
andhowaerosolactivationistreated.KOHmeansthatmodified agulationbyredistributingN andM intothirtybinsbutkeeps
k k
Ko¨hler theory was used for cloud processing and wet deposi- fifteenbinsforcondensation.
tionasisthecaseintheTOMAS-30model.IncontrasttoKOH, Appropriate pairs of simulations are used to estimate each
constant activation diameter (CAD) is used to exclude cloud- process-specificerrorwiththeirnumberormassconcentrations
processingerrors;theactivationdiameterissetto∼30nmfor (see third column in Table 2). All types of error except the
convective clouds and to ∼70 nm for large-scale clouds. To offline CCN error are based on total aerosol number (defined
ensureidenticalemissionsinputs,allsimulations(exceptCAD- as CN10, number of particles larger than 10 nm in diameter),
686 Y.H.LEEANDP.J.ADAMS
CN70(samebutfor70nmindiameter),andCN100(samebut TOMAS-12models(i.e.,aratioofaerosolnumberandmassof
for100nmindiameter).CN70andCN100arechosentoreflect CAD-15 or CAD-12 to CAD-30) in Figure 4. Except for sea-
typicalcriticaldiametersforparticlestoactivate,especiallyfor saltmass,alldifferencesshowninFigure4aredueprimarilyto
stratiformcloudswithsupersaturationsof∼0.2%. the purely numerical “microphysics” error of using fewer size
binsforcondensationandcoagulation.Sulfatemassconcentra-
5.2. 3-DModelEvaluationofFastTOMAS tionsandCN10numberconcentrationinTOMAS-15/TOMAS-
Three-dimensional simulations using TOMAS-15 and 12 show very similar results (within ±5% in most regions) to
TOMAS-12 in a global model are evaluated against the TOMAS-30. Sea-salt mass concentrations show large changes
TOMAS-30 model. Here, we report simulation results from a inTOMAS-12thataremostlycausedbydifferencesinthelast
3-monthaveragefromMarchtoMayafterdiscarding3months size bin, i.e., particles larger than ∼3 μm. Unlike sulfate and
ofmodelspin-up.A3-monthsimulationispreferredtoa1-year carbonaceousaerosols,significantnumbersofsea-saltparticles
simulationtosavecomputationaltimeandbecausethenumeri- arefoundinthecoarsemode,wheredrydepositionisthemain
calerrorsareverysimilarmonthtomonth.Figure3showsthe removal process. Since dry deposition is a strong function of
3 emissionerrorcausedbychangingtheemissionssizeresolution particlesize,adifferentmeandiameteratcoarsebinsresultsin
01 from thirty bins to fifteen bins but otherwise using the higher, verydifferentdrydepositionrates.Asaresult,errorsinsea-salt
2
pril tehrrirotrys-bairneraepsoplruotxioimnaftoerlyalwl oitthhienr±pr2o%cesfsoers.CENm1i0s,siConNs7-r0e,laatnedd maearosssoclonfocernTtrOatMioAnsSa-1re2,lawrgheircthhaunsefsorosnullyfat2esoirzcearbbinosnaicneothues
A
6 CN100predictionsinmostoftheregionsasshowninFigure3. coarsemode.InFigure4,microphysicserrorsdisplaysomelat-
1
7 Three-month averages of mass of sulfate, sea-salt, organic itude patterns: negative errors near the equatorial regions for
4
4: matter, and number concentration (CN10) in the lowermost OMandCN10,andincreasingerrorsfrommid-tohigh-latitude
at 1 vertical layer are compared in TOMAS-30, TOMAS-15, and regions in Northern Hemisphere for all species except sulfate.
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FIG.5. Globaldistributionofmicrophysicserrorofsurfacelayer(a)CN70,and(c)CN100,andcloud-processingerrorof(b)CN70,and(d)CN100,respectively.
Notethatthecloud-processingerrorisdefinedhereaserrorsresultingfromlowersizeresolutionusedinwetdepositionandcloudprocessingandisestimatedby
makingaratioofKOH-15toKOH-30andthenbysubtractingmicrophysicserror.Notethatthelowerlimitonthecolorbarisdifferentfromthoseinotherfigures
becausetheminimumerrorinthisfigure(Figure5)exceedsthatlimitandthevalueonthetoprightofeachfigureisaglobalaverageoftheerrorsdisplayedinthe
map.(Colorfigureavailableonline.)