Oct 27, 1997 - copy of the nucleation code send email to AT. References. Adamson ... Hare, D. E., and C. M. Sorensen, Raman spectroscopic studies of bulk.
JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 102, NO. D20, PAGES 23,845-23,850, OCTOBER 27, 1997
A model description for cirrus cloud nucleation from homogeneous freezing of sulfate aerosols Azadeh Tabazadeh
and Eric J. Jensen
NASA Ames Research Center, Moffett Field, California
Owen B. Toon Laboratory for Atmospheric andSpacePhysics, Universityof Colorado,Boulder
Abstract. Classicalnucleationtheoryfor homogeneous freezingas well asrecentlaboratorydata areusedto formulatean algorithmfor ice nucleationfrom an aqueoussulfuricacidsolution droplet.A newpammeterized functionis derivedfromre•nt thermodynamic datato expressthe variationof stflfiafcacid solutioncompositionwith temperatureandrelativehumidity.This functionis thenusedto derivecriticalice nucleationparameters fromrecentlaboratorydata.The criticalnucleationparameters areusedin a classicalnucleationtheoryto derivethediffusion activationenergyof watermoleculesin a sulfuricacid solutionfrom the measurements. The deriveddiffusionactivationenergyof watermoleculesin a sulfuricacidsolutiondoesnot agree with the diffusionactivationenergycalculatedfrom a viscousflow formulationthat is commonly used in classical nucleation rate calculations. Our restfits show that ice nucleation in a stdfate
dropletoccurswhenthe interfaceenergyof ice againstthe stdfatesolutionis approximately17 dyn cm4. We calculatethata supersaturation ratioof about1.3 to 1.5 is requiredto nucleateice from an aqueousstdfuricacidsolutiondropletin the temperature rangeof about185 to 240 K. This supersaturation corresponds to a supercooling of a stdfatesolutionto about2 to 3 K below the equilibriumcondensation pointof ice. Simplefunctionsare givenfor estimatingthe nucleation pointof ice in theuppertroposphere. The differencesbetweenpreviousparameterizations andthis work are discussect
1. Introduction
about-40øC[e.g.,Pruppacher andKlett,1978;Pruppacher, 1995]. On the other hand, cirrus clouds usually nucleateat
Cirrus clouds cover about 35% of the Earth's surface and
thus have an important influence on climate through their effect on the radiationbudget[Ramanathanet al., 1983; Liou,
around-80øCto-40øCdepending on the relativehumidity conditions[Jensenet al., 1994a; Heymsfield and Miloshevich, 1995]. Thus the current laboratorydata on ice nucleationin
1986; Jensenet al., 1994a, b]. Recent studiesalso indicate that supercooledwater are not suited to adequatelyaddresshow cirruscloudsmay play a significantrole in the heterogeneous cirrus cloudsmay form in the upper troposphere.Currently, chemistryof the upper troposphere[Borrmannet al., 1996]. only a few laboratory groups have measuredcritical ice parameters in aqueousH2SO4aciddroplets[Bertram One of the most poorly understoodaspectsof cirrus cloud nucleation formation is how such ice particles nucleate in the upper et al., 1996; Imre et al., 1997]. Here we use classicalnucleation troposphere.There is growing evidencefrom field observa- theoryalongwith the laboratorydataof Bertramet al. [1996] tions that the nucleation processoccurs by homogeneous to parameterizean algorithm for ice nucleationfrom an H2SO4acidsolutiondroplet. freezing of ice in an aqueousH2SO4 acid solution droplet aqueous [Sassen and Dodd, 1989; DeMott et al., 1994; Jensen et al.,
1994a; Heymsfield and Miloshevich, 1995]. There are modeling,laboratory,and field studiesto supportthe fact that H2SO4 acid aerosolscan remain supercooledto very low temperatures [Dye et al., 1992; Tabazadeh et al., 1994; Carslaw et al., 1994; Anthony et al., 1995]. Thus when ice saturation is reached in the atmosphere,nucleation of ice particlesmostlikely occursfrom an aqueoussolutiondroplet. Most of the laboratory work over the last 50 years has focused on measuring ice nucleation rates from a pure supercooledwater droplet, which can remain liquid to only Copyright1997by the AmericanGeophysical Union.
2. Model Description DenotingVa (in cubiccentimeters) and ws as the volume andweightpercentof an aqueoussulfatesolutiondroplet,we find the rate of ice nucleationat a giventemperature,
j(T, w, Va) =C(T, ws, Va) EXP [-z•f'g -•aCt ] kT
(1)
whereC (in particlesper second)is the preexponential factor,
AFs (in ergs)is thefreeenergy fortheformation of theice germ, AFa½ t (in ergs) is the diffusionactivationenergyof
Papernumber97JD01973. 0148-0227/97/97JD-01973509.00
water molecules across the ice/sulfate solution phase boundary, and k is the Boltzmann constant. The pre23,845
23,846
TABAZADEHET AL: CIRRUSCLOUDNUCLEATIONFROMHOMOGENEOUSFKEEZ•G
moleculesin supercooledwater below 240 K does not agree with a viscousflow formulationas describedby Pruppacher [1972]. Basically, below 240 K, water molecules in a supercooled solutionforma networkof clusters,andthe sizeof C(T, ws, Va)_--2.1xlO33Va4osut/ice(ws,T)T (2) suchclustersincreaseswith decreasein temperature.A number of spectroscopic studiessupportthe idea of clusterformation where o•a/ice is the interface energy betweenthe ice/sulfate in supercooledwater [e.g., Bansil et al., 1982; Hare and solution. For a fixed droplet size the variations of C with Soerensen, 1990; Pruppacher, 1995]. From these studies, temperature and dropletweightpercenthaveonly a negligible Pruppacher [1995] recently suggestedthat the diffusion effect on the nucleation rate calculations. activation energy of water moleculesacrossthe ice/water The free energyterm is givenby interfacein supercooled waterbelow240 K shouldbe estimated from the transferof water clustersacrossthe phaseboundary 4 insteadof the transferof singlewater moleculesas formulated previously[Pruppacher,1972]. Thus if the diffusionof water moleculesin a cold aqueoussulfuricacid solutionoccursby the
exponentialfactor is estimatedas [Pruppacher and Klett, 1978]
at,(r, =
(3)
wherers, (in centimeters) is thecriticalgermradius, defined as [Jensenet al., 1994a]
rs =
2Mwosa/i½e(ws,T)
(4)
transfer of water clusters across the ice/solution interface, then
(7) cannotbe usedto estimatethe diffusionactivationenergy of watermoleculesin solution.To avoidthisproblem,herewe derive l•'act directly from some recent ice nucleation experiments in sulfuricacidaerosols[Bertramet al., 1996].
p,½,(T)[L,•(T)ln Tf+IR(T +Tf )lnaw(T) 1 T
2
2.1.
Aerosol
Composition
where M• is the molecular weight of water (in grams per Commonly, the Gmitro and Vermeulen [1964] vapor mole), @e,is the ice density(in gramsper cubiccentimeter), pressurerelations for sulfuric acid are parameterizedinto a
Lmis thelatentheatof icemelting(in ergspermole),Tf is
function
in order to calculate
the variations
of sulfuric
acid
the ice melting temperature(273.15 K), R is the universalgas constantand a• is the water activity. The latent heat and densityrelationsare given in the appendix.The wateractivity or the ambientrelative humidityis calculatedby dividingthe
aerosolcompositionwith relative humidity and temperature [e.g., Steele and Hamill, 1981]. However, recent studies indicatethat theseparameterizations could underestimatethe water activity over a given sulfuric acid solutioncomposition atmospheric watervaporpressure (PH2o)overtheliquidwater by about10% [Massucciet al., 1996; Tabazadehet al., 1997a] saturation vapor pressure (PH2o, seetheappendix). since the original vapor pressurerelations of Gmitro and The diffusion activation term is approximatedfrom the Vermeulen [1964] are optimized to obtain better agreement viscosityof the sulfatesolutionby [Pruppacher, 1972] with high-temperaturevapor pressuredata. Thus we do not recommendusing such parameterizationsto predict aerosol compositionat cold temperatures, which are of interesthere. AFa½ t=k T (5) Recently,Cleggand Brimblecombe[1995], usinga widerange of thermo-dynamicdata in the temperaturerange of
