GEOPHYSICAL RESEARCH LETTERS, VOL. 27, NO. 4, PAGES 521-524, FEBRUARY 15, 2000
Ice Nucleation in Cirrus Clouds: A Model Study of the Homogeneous and Heterogeneous Modes KennethSassenand Sally Benson Departmentof Meteorology,Universityof Utah
Abstract. Parcel cloud model simulations have explored the feasibility of a unified approachto describethe homogeneous and heterogeneous ice nucleationmechanismsin cirrus clouds. It was assumedthat the ice crystalgenerationprocessinvolved the freezingof ammoniumsulfate haze particles, as modulated by an effective temperatureproportional to molality in both cases. Treated as variables in the -36 ø to -60øC model domain
are the updraftvelocity, and the terms in a modified Fletcher equation used to approximate heterogeneous freezing. Parameterizationsdrawnfrom the homogeneousfreezing runs are providedfor the threshold relative humidity and numberof crystalsnucleated,as functionsof both temperature and updraft velocity. We find that heterogeneousnucleation can compete or dominateat relatively weak updrafts,but only for unusually high ice nuclei concentrationand temperatureactivationterms. Introduction
Until relatively recently,researchinto the nucleationof ice in the atmosphere emphasized the processes leading to precipitation, and the methods to artificially increase the efficiency of precipitation in mixed phase clouds. Hence, attentionwas given to the variousmechanisms[Vali, 1985] by which supercooledcloud dropletscould freezeheterogeneously into ice crystalsthroughthe intervention of special ice nuclei (IN) particles. The situation with regard to the formation of cirrus clouds, however, is quite different. Here we are confrontedwith a paradox causedby the action of the rapid nucleation processesthat occur at temperaturescolder than about-40øC. Since liquid water can not exist in the frigid upper troposphere (UT)long enough to grow into cloud droplets,how thencan cirrusform? The solution to this dilemma came from examining the initial stage of clouddroplet formation, which is commonly initiated on hygroscopicparticlesor aqueousacid drops. This involves the precursorsto cloud droplets,haze particles, which are minute solutiondropsthat remain in equilibrium with their environment, swelling or shrinking in response to relative humidity (RH)changes. The importance of haze particles for cirrusis that concentratedsolutions inhibit the particles from freezinguntil dilution occurs. The solutiondrop temperatureis thus transformedinto a warmer effective temperatureTe• for evaluatingthe nucleationrate [Sassenand Dodd, 1988 hereafter SD88], Although the relative importanceof the two nucleation mechanismsin cirrus is a matter of debate [Khvorostyanov and Sassen, 1998a], both processesshould be affected by the freezing point depressioneffects of concentratedsolutions. In this numericalstudy, we considerIN to act as catalysts that increasethe inherenthomogeneousnucleationrate, and so as a first order approximation, assumethat solution strength
actsequallyin bothnucleation processes.In otherwords,the conceptof Teffappliesequally.The purposeof this process
studyis to evaluatethe relative contributions to cirrus cloud formation that result from the homogeneousand heterogeneous nucleationmodesunder this scenario. In addition, we develop parameterizationsfor relationships between updraft velocity, temperature,and ice crystal concentrations in cirrus clouds to improve the treatmentof ice production in large scale models. We begin with a brief descriptionof the parcelmodel usedhere. The Cloud
Model
The parcel cloudmodel was developedfor interpreting in situ and polarizationlidar measurementsof the phasechangein a highly supercooledliquid wave cloud [SD88], and has since seena numberof applications, This adiabatic model considers microphysicalprocessexplicitly, treating each haze particle and ice crystal individually at model time steps as small as 0.01-s to ensurestability during periodsof rapid phasechange. A model option usedhere deals with the removal of nucleated ice crystals from the updraft based on a vertical wind shear mechanism [Sassen and Dodd, 1989, or SD89], which allows
RH to again increase. Although this approachis artificial, during a single model run a series of temperature-dependent nucleation "impulses" are generated as the ice crystals are allowed to sedimentout of the 100-m diameter updraft. The wind shear rate is varied
of nucleation
1030 ß
_----,
1025' '
PK97
x
KS98
o 1020 -r
15
d 10
,,
............SD88
-
•
0 • 101
••
1
05
z
100 10-5 -50
•
[
-45
I
•
s
,
I
-40
....
I
....
-35
\
-30
Temperature(øC)
Copyright2000 by theAmericanGeophysical Union.
Figure 1. Comparison of the nucleationratesfor pure water.
Papernumber1999GL010883. 0094-8276/00/1999GL010883
such that the number
impulsesare approximatelythe samefor each model run. In the currentcase,we treat the ice nucleationprocesseither as purely homogeneous(i.e., the UT lacks significant numbers of IN) using the Khvorostyanov and Sassen [1998b, or KS98] nucleationrate Jls,or as a competitive processinvolving both homogeneousand heterogeneousfreezing. Figure 1 compares the theoretical values of Jlsused in this study with that of Pruppacher and Klen • [1997, or PK97], and the SD88 measurement-basedcurve, where it can be seen that despite significant differences at the lowest temperatures, the
$05.00
521
indicated
homogeneous
agreementnear -40øC is reasonable. As we shall see, this is important becauseof the strong influence of Te,, which in essencelimits the effective nucleation temperatureto --38øC (where the measurements in SD88 were obtained). As for heterogeneous nucleation,it is typically treatedas a temperature-dependent process,explainableby the following equationbasedon the parameterization of Fletcher [1969]: Nht(T)= Aoexp(-AzZ)exp [Bs(Ts-T)] , (1) where the temperature-dependent increase in IN activation Nht(T) is traditionallyregulatedby the constantsAo and Bs,and the amountof supercoolingbelow Ts=0øC. The middle term was addedby Sassen[1992] in an attempt to accountfor the vertical decline in IN with height, based on the assumption that IN are relatively large particles derived from the Earth's
RHw(with respectto water), and -36.0øC temperature. Clearly, our parcel model can not realisticallytreat the consequences of precipitation or structuralcloud development. However, by modelingthe cirruspropertiesinitiated in this environment, we hope to better understandthe basic factors involved in cirrus formation, with the possibleapplication of our findings within the greaterframeworkof GCSS model research.
Homogeneous Nucleation Results
The objective of these simulations was to assess the relationship between ambient temperature,updraft velocity, and nucleated ice crystal concentration, and basically to determine whether this cirrus developmental process is surface [Sassen, 1989]. This correction factor was neededto amenableto parameterization.Runningthe model in the SD89 explain polarization lidar observationsof highly-supercooled version,the amountof wind shearwas varied suchthat duringa liquid altocumulus cloudsin the middletroposphere.A value of particular run at constant updraft velocity U, a sequenceof Az=0.75 km'l was offered as an estimationbecauseit nucleation events were modeledspanning the -36 ø to -60øC corresponded to the general height dependencynoted in the temperaturerange, thus reducing the computational effort. vertical distributionof large and giant aerosols[Warnek, 1988 AftervaryingU between0.04 to 1.0 m s-1,an arrayof model Figure 7-25], and alsocould accountfor the lidar observations. predictionswas obtained,leading to our parameterizations. Shownin Figure 2 is a typical set of model resultsusing the In practice,we vary Bs and Az within reasonablelimits, and employ for droplet temperatureT in Eq. 1 the same effective above initial conditions and U=0.3 m s-s. The number of ice haze particle temperature as for homogeneous nucleation crystalsnucleatedhomogeneouslyNhm(shown as the total N,), variations in RHw, effective J•sbasedon Telf, and the relation [DeMott et al., 1998], given by Tel• = T + X fiT, (2) betweenthe ambient and haze particle effective temperatures whereX=l.7 relatesthe freezing-to-mel.ting point depressions are shownas a functionof height. With decreasingT, for each of impure ice, and fit is the melting point depression nucleationimpulse(causingthe steps in N) Nhmincreases,the proportional to the molality of the solution drop [SD88]. peak RHw decreases,and the effective Jl• increasesslightly. Thus, Tetfaccountsfor the tendencyof solutionsto supercool These resultsconformwith SD89, but note the behavior of more strongly than pure water becauseof the effects of the (dashedcurve), which is near constantat the time of nucleation dissolvedmaterials. Values appropriatefor ammoniumsulfate regardlessof the ambientT. Thus, despitethe differencesin Jls are used,employingthe skeweddry massdistributiondescribed in Figure 1, it follows that if the critical T•ffremainsat --38øC in SD88 at a total concentrationof 200 cm-3. In other words, then all threeJ• curveswill yield similar results. Replicating such results for a series of model runs with the model findings are aimed at haze particles derived from varyingU leadsto the following resultsand parameterizations: ammoniated aerosols(with or without the inclusion of an IN), which currentknowledgeindicates are important cirrus cloud a) Regression analysis of the dependenceof ambient temperature (T, øC)onthreshold RHwasa function of U (ms forming nuclei [Tabazadehand Toon, 1998]. The initial modelinputsarebasedon the genericcirruscloud between-40ø to-60øC yields the following relationship: RHw=aT+b, (3) atmosphericprofiles offeredas a test case for the GEWEX
CloudSystemStudy(GCSS)Working Group2 [Starr,personal wherea =-1.119x10 -4U + 5.31x10-3,andb = 2.05x10-2 U + communication,1998]. A level of the profile whereadiabatic 1.182. This agreeswith the averagerelationship RHw = ascent would initiate a cirrus cloud was used to initialize our (4.93x10-3) T + 1.17 developedin SD89 when updraftsof model,corresponding to 8.0 km height,361 mb pressure,65% -0.15 m s-• areinsertedin Eq. 3, whichfor many large-scale 10.5
-60
10.0
-55
-50 •
9.0
-45 •
8.5
-40
8.0 0
3
6
9
N, (cm'3)
60 70 80 90-60
RHw(%)
-40
-20
T (øC)
10"'
10-'
10'
Jls(cm-'s-')
Figure 2. Typical resultswithin the modelheightdomainfor, from left to right, the total numberN, of ice crystals nucleatedhomogeneously in successive impules,relative humiditywith respectto water, ambient(solid) and effective (dashed)temperatures,and the effective homogeneous nucleationrate.
SASSEN AND BENSON:
ICE NUCLEATION
IN CIRRUS
CLOUDS
523
Note the distinctbehaviorsof Jlsfor the two modes. As a result
model applicationsmay remain an adequatedescription.
b) Thedependence of the crystalconcentration cm'3nucleated of homogeneouslyin each impulsesobeys the relation,
N•n= (X exp(• T), wherethe resultsof regressionanalysesfor (• and • are:
(4)
for U > 0.3 m s'•
(• = 1.545U2 - 0.668U+ 0.0959, • = 0.036U - 0.0913, and for U < 0.3 m s-•
(x = -0.272U2 + 0.177U+ 0.00049,• = -0.1415U- 0.043. c) An aspectimportant to the application of our findings in larger scale models involves the rapidity of the haze-to-ice particletransformationin relation to typical modeltimesteps. Our results show that although the updraft velocity has an influence, the phase transformationin any particular impulse takesonly on the order of 0.5-1.0 min to complete. Thus, the homogeneousnucleationimpulse period is comparableto the relatively short time steps in mesoscale models, but is considerablyshorterthan thoseusedin larger scalemodels. We stressthat theseparameterizationsrepresenta first step and are valid only for initial cirrus formation in relatively icefree air: a large range of conditionswould be found in cirrus as haze and existing ice particles compete for the available moisture, including prohibiting new nucleation even within strong updrafts. Although our approach uses an aerosol population that is gradually depleted with ice crystal nucleationand fallout, the reservoir of haze particles modeled is sufficientto avoid affecting significantly the results. The slightdecreasein Teffin Figure2, however,may result from the selectiveloss of the largest aerosolparticleswith time.
the differences in the action of the two mechanisms, the
heterogeneous Jlsrate beginsto increasesoonerbut lessrapidly than the "spikes"apparentin the homogeneousrate. Thus the heterogeneous processinitially dominates,until it is replaced at coldertemperaturesby homogeneousfreezing. Nonetheless, under the assumption that Teef applies equally to both nucleationmodes,it is apparentfrom Table 1 that it is only under favorable (i.e., for IN activation) conditions that the heterogeneous processmay be of importancein cirrus. Table 1 reveals the contributions
of the two mechanisms
in
termsof the total numberof crystalsnucleatedhomogeneously Nhmand heterogeneouslyNht between-40 ø and-60øC, as functionsof U, Az, and Bs. Note that for Bs=0.4 or less, only homogeneous nucleationoccursunder this range of conditions, and that the concentrationsare somewhat arbitrary becausethe number of impulses varies. Under "typical" heterogeneous
conditions(Az=0.75km-•, Bs=0.4-0.6), the homogeneous mode shouldprevail in cirrusformationexcept,perhaps,at the
cm s-• scaleof slowstableuplift. This situationdiffersonly if the relatively extremeB•=0.8 is used(as in Figure 3), or if no height dependence in IN (Az=0) is treated, in which case the heterogeneousmodealways dominates. Using B•=0.8 and a reductionin IN with height (Az=0.5-0.75), the heterogeneous mode acts first at low U and higher T until the homogeneous modetakesover at higherU and lower T. When IN are scarcer (Az-l.0), the homogenousmode is not much affectedand Nht
represents a minorbackground contributor for U>0.07m s-1.
The interplay of Nhmand Nhtas a function of U in Table 1 shows some interesting features. In contrast to the strong Mixed Homogeneousand HeterogeneousResults increase in Nhmwith increasing updraftsknown from previous In view of the uncertaintiesassociatedwith specifying the studies and confirmed by Eq. 4, Nhtdoes not show much constantsin Eq. 1, to evaluatethe competitive effects caused sensitivity to U, and may actually decreasewith increasing by heterogeneousfreezing we took the approachof varying updraft. When both modesact together,homogeneousfreezing theseparametersover reasonablelimits. That is, from Fletcher usually dominates. The competition between the two modes [1969], Bs was varied from 0.2 to 0.8, and the height- apparently acts in a complicatedway, in which the initiation dependent parameterof $assen[1992]Az wasvariedfrom 0 (no of each nucleation sequencemodulates RHw and so affects height dependence) to 1.0 (a strong dependence). Note that subsequentcrystal production. Further effort is required to whatcanbe considered as "typical"valuesfor theseparameters determineif a reliable parameterization of the action of the
are0.4-0.6and0.75km-• respectively, whileAo 10'5 L-•.
combined
Since the factor A• is designedto reducethe impact of the surfaceIN sourcefunction,Ao couldbe treatedas a constant. We show in Figure 3 a comparisonof heterogeneousplus homogeneousmodelpredictionsfor a casethat yields strong
Conclusions
competitive results:Az=0.75km4 andB•=0.8,for U=0.3 m s'•.
10.5
-60
10.0
-55
modes is feasible.
These results are intriguing in that after employing a reasonablescenariofor treating heterogeneousnucleation, we find that the two freezingmodescan competesuccessfullyonly under relatively extreme conditions associated with the modifiedFletcherequation. In otherwords,unlessthe factor B• lies near the usual upper limit established by ground-based research, and the concentrations of IN are similar to those
measuredat the surface, homogeneous nucleation should dominate in cirrus clouds. To evaluate these competitive effects we have assumedan exponential height dependencein 9.0 the availability of IN, without which the homogeneousmode would dominatecirrusformation except at the highest vertical 8.5 velocities. Moreover, we have ignored laboratory findings indicatinga time dependencyin the activationof at least some 0 1 2 3 4 5 6 60 70 80 90-60 -40 -20 10" I0 • 10' types of IN [DeMott et al., 1983], since the framework to treat N, (cm') RHw(%) T CC) J• (cm's') this processkinematically has yet to be createddespite the recent major strides in the theory and parameterization of Figure 3. Typicalmodelresults,as in Figure2, exceptthat homogeneousnucleation [PK97; KS98]. boththe homogeneous (solid lines) andheterogeneous (dotted These findings reflect the fundamental differences in the lines)modesare simulated. The dashedline in the N• panel is underlyingphysicsinvolved in the two processes. Neglecting the total numberof crystalsnucleated. molality effects, whereas homogeneous nucleation is a 9.5
8.0.................................................... •,• ................... !', ............
524
SASSEN AND BENSON: ICE NUCLEATION
IN CIRRUS CLOUDS
Table 1. Comparison of totalnumbers (cm'3)of ice crystals haze particlescontaining IN. Few in situ measurementsof IN nucleatedhomogeneously.(Nhm)and heterogeneously(Nht) while varyingthe updraftU andtermsin Eq. (1). The N arethe sum of all particlesnucleatedin successive impulses. U (m s'l) 0.03 0.07
0.3 0.7 1.0
Bs
Az = 0 Az = 0.5 Az = 0.75 Nhm Nht Nhm Nht Nhm Nht
Az = 1.0 Nhm Nht
0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8
0 0 0 0 2.2 0 26.8 0 50.6 0
0.5 0.2 0.6 0.2 11.7 9.6 32.3 31.8 57.0 56.2
4.8 56.0 2.3 64.2 2.7 43.8 2.2 37.4 1.5 35.6
0.5 0 0.6 0 11.7 0 33.1 6.0 37.1 21.4
0 18.1 0 !0.9 0 5.9 0 12.5 0 12.8
0.5 0 0.6 0 11.7 4.1 33.3 33.5 57.0 46.0
0 2.3 0 1.2 0 2.7 0 3.9 0 3.3
0 0.3 0 0.2 0 0.5 0 0.5 0 0.5
in the UT are available, although Rogers et al. [1998] suggest that they are highly variablein time and space. Ultimately, we needto improveour knowledgeof the sourceand abundanceof upper tropospheric IN to better comprehend nucleationcontrolledcloud microphysicalproperties,which are likely to have significantradiative consequences. Acknowledgments. This researchhasbeenfundedby NSF grant ATM9528287, and DOE grant DEFG0394ER61747from the Atmospheric RadiationMeasurementprogram.
References
DeMott,P. J., W. G. Finnegan,and L. O. Grant,An application of chemicalkinetictheoryand methodology to characterizethe ice
nucleatingpropertiesof aerosolsusedfor weathermodification,J. ClimateAppl.Meteor.22, 1190-1203,1983. functionof temperature, dropvolume,and time, heterogeneous DeMott, P. J., and coauthors,The role of heterogeneousfreezing nucleationin uppertroposphericclouds:Inferencesfrom SUCCESS, nucleationis essentiallycontrolledby the cooling rate. Thus Geophys.Res.Lett. 25, 1387-1390, 1998. one may expectthat the interplayof the two modesmay create significantvariationsin cirruscloudcontent(i.e., crystalsize Fletcher,N.H., ThePhysicsof Rainclouds,CambridgeUniversityPress, pp. 229-258, 1969. and concentration)as a functionof the ascentrate, as relatedto Heymsfield,A. J., andL. M. Miloshevich,Relativehumidityand temper-
meteorologicalconditions. A similar dependence on vertical velocityhasbeenindicatedin the modelresultsof Jensonet al. [1994] and DeMott et al. [1998]. In both nucleationmodes,we have assumedthat the freezing
ratesaremodulatedby hazeparticlemolalitythroughthe use of an effective temperature. We acknowledgethat this is an estimation, and that large uncertainties also exist in specifyingthe parameters in Eq. 1. However,the efficacyof usingTeff is supported by the fact that if hazeparticlesarenot significantlywarmedin this way, the particleswouldfreezeat deliquescenceand totally transform the cirrus formation process.Althoughour approach shouldbe examinedfurther,it is currentlya convenient tool for approximatingthe effectsof chemistryon cirrusformation. Anotherconsequence of using Terris that despitethe three divergenthomogeneousJlscurves for pure watershownin Figure1, it is onlytherelativelyminor
ature influences
on cirrus formation
and evolution:
Observations
from wave clouds and FIRE-II, J. Atmos. Sci. 52, 4302-4326, 1995.
Jensen,E. J., O. B. Toon, D. L. Westphal,S. Kinne, and A. J. Heymsfield, Microphysicalmodelingof cirrus, 1. Comparisonwith 1986 FIRE IFO measurements, J. Geophys.Res.99, 10421-10442,1994. Khvorostyanov, V. I., and K. Sassen,Cirrus cloud simulationusing explicitmicrophysicsand radiation.Part I: Model description, J. Atmos. Sci. 55, 1808-1821, 1998a.
Khvorostyanov,V. I., and K. Sassen, Toward the theory of homogeneous nucleationand its parameterizationfor cloudmodels, Geophys.Res.Lett. 25, 3155-3158, 1998b. Pruppacher,H. R., and J. D. Klett, Microphysicsof Clouds and Precipitation,pp. 191-215,Kluwer, Boston, 1997. Rogers, D.C., P. J. DeMott, S. M. Kreidenweis, and Y. Chen, Measurements of ice nucleating aerosols during SUCCESS., Geophys.Res.Lett. 25, 1383-1386, 1998. Sassen, K., Ice nucleiavailabilityin thehighertroposphere: Implications differences at ~-38øC that matter. This results from the of a remote sensingcloud phase climatology,in Nucleation and Atmospheric Aerosols,editedby N. Fukutaand P. Wagner, pp. 287characteristic Teff at which homogeneous freezing occurs 290, DeepakPublishing,Hampton,Virginia, 1982. regardless of ambienttemperature: thusthe large differencesat coldertemperatures are of only academicinterest, since, after Sassen,K., Reply.,J. Atmos.$ci. 46, 2346-2347, 1989. Sassen,K., and G. C. Dodd, Homogeneousnucleationrate for highly all, purewaterdropscannot existat suchlow T. supercooled cirrusclouddroplets,J. Atmos.Sci.45, 1357-1369,1988. There is also the unresolved question of the relative Sassen,K., and G. C. Dodd, Haze particle nucleation simulations in importanceof other materials, such as sulfuric acid, which cirrus clouds,and applicationsfor numerical and lidar studies,J.
display different chemicalpropertiesrelatedto nucleation. Atmos. Sci. 46, 3005-3014, 1989. Nonetheless,sulfateparticlesprobably representan abundant Sassen,K., and coauthors,The 5-6 December 1991 FIRE IFO II jet sourceof cloud-formingparticles in the UT, which can be streamcirruscasestudy:Possibleinfluencesof volcanicaerosols,J: Atmos. $ci. 52, 97-123, 1995. derived from either boundary layer or stratosphericsources [Sassenet al., 1995]. We would alsolike to point out that the Tabazadeh, A., and O. B. Toon, The role of ammoniated aerosols in cirruscloudnucleation,Geophys.Res.Lett. 25, 1379-1382, 1998. action of sulfates is not necessarily limited to temperatures warmer than --65øC, where the modeled threshold nucleation
Vali, G., Nucleationterminology,Bull. Amer. Meteor. Soc. 66, 1426, 1985.
RHw and deliquescencepoints converge. Rather, after Warneck, P., Chemistryof the Natural Atmosphere,pp. 360-373, deliquescence,haze particle recycling through drier air will AcademicPress,New York, 1988. leave wetted aerosols down to RHw--36% available for ice nucleation,until further drying inducesefflorescence. K. Sassen,135 S 1460 E 819 WBB, Universityof Utah, Salt Lake O• current state of knowledge of cirrus cloud generation City, UT 84112. (e-mail:
[email protected]. utah.edu) [Heymsfieldand Miloshevich, 1995] implies that they do not form in slightly ice-supersaturated air, that is, from the direct (Received:June29, 1999; revised:November 26, 1999; accepted:6 depositionof vapor onto IN or the freezing of newly-activated January,2000)
