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Strong dependence of cubic ice formation on droplet ammonium to sulfate ratio. Murray, Benjamin J.; Bertram, Allan K. 2007-08-31

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Strong dependence of cubic ice formation on droplet ammonium tosulfate ratioBenjamin J. Murray1,2and Allan K. Bertram1Received 27 April 2007; revised 31 May 2007; accepted 28 June 2007; published 23 August 2007.[1] We show that the phase of ice that crystallizesin solution droplets, under conditions relevant for theupper troposphere (UT) and tropopause region (typically>188 K), is strongly dependent on the ammonium tosulfate ratio (ASR) of the solute. Droplets of aqueous(NH4)3H(SO4)2(ASR = 1.5) freeze dominantly to cubicice over a range of temperatures relevant for the UT andtropopause; whereas aqueous NH4HSO4(ASR = 1.0)droplets do not freeze dominantly to ice Icat temperaturesrelevant for the UT and tropopause region. We also showthat the amount of cubic ice formed in the aqueoussolution droplets at temperatures below 200 K isindependent of droplet size, whereas a size dependencewas observed at higher temperatures. The implications ofthese results for the phase of ice that forms in uppertropospheric ice clouds and the potential impact onclimate, water vapor, and ozone are briefly discussed.Citation: Murray, B. J., and A. K. Bertram (2007), Strongdependence of cubic ice formation on droplet ammonium tosulfate ratio, Geophys. Res. Lett., 34, L16810, doi:10.1029/2007GL030471.1. Introduction[2] Ice clouds that occur in the Earth’s upper troposphere(UT) and tropopause region play an important role in theEarth’s climate by scattering and absorbing radiation. Inaddition, they influence the distribution of water vapor inthe troposphere as well as the amount that enters thestratosphere, where changes in humidity may have impor-tant consequences for polar stratospheric ozone [Jensen andPfister, 2005]. Ice clouds in the UT and tropopause region,including cirrus and cirrostratus, influence the chemistry ofthe atmosphere by providing a surface on which heteroge-neous chemical reactions can occur [Abbatt, 2003]. Despitethe potential impact of ice clouds on the planet’s atmosphereand climate, many important details regarding their forma-tion mechanisms and microphysics remain poorly under-stood [DeMott, 2002; Penner et al., 2001].[3] A significant mechanism of ice cloud formation in theUT and tropopause region is thought to be homogeneousfreezing of submicron aqueous droplets [DeMott, 2002].Recently it was shown that the metastable cubic crystallinephase of ice (ice Ic) was produced when a range of solutiondroplets froze homogeneously under conditions that wererelevant for the UT and tropopause [Murray et al., 2005].Previous to this work, it was often assumed that only thestable hexagonal phase (ice Ih) would form under conditionsrelevant for the UT and tropopause [Pruppacher and Klett,1997].[4] Recent laboratory measurements have shown cloudscomposed of ice Icwill have a saturation vapor pressure11 ± 3% larger than that of a cloud composed of ice Ih[Shilling et al., 2006]. Hence, the formation of cubic ice inthe UT and tropopause region may have some importantimplications: Murphy [2003] has shown that the differencein vapor pressure between ice Icand ice Ihmay stronglyinfluence cloud properties and lifetimes through a processanalogous to the Bergeron-Findeisen process in whichhexagonal ice crystals grow at the expense of metastablecubic ice crystals. Jensen and Pfister [2005] examined theimpact of persistent high ice supersaturations in cold cirrusclouds. They found that transport of water into thestratosphere is enhanced and cloud properties were altered.Also, a recent laboratory investigation revealed that cubicand hexagonal ice have different heterogeneous chemis-tries [Behr et al., 2006], which may have importantimplications for the processing of gas phase species byice clouds.[5] As mentioned, recently it was shown that ice Icwasproduced when a range of solution droplets froze homoge-neously under conditions that are relevant for the Earth’satmosphere [Murray et al., 2005]. However, the effect of thesolute type on the amount of Icproduced was not studied indetail. Moreover, the effect of droplet size on the amount ofIcformed in aqueous solution droplets was not explored.The size dependence is important for extrapolating labora-tory data to the atmosphere, since laboratory measurementswere performed on supermicron droplets, whereas freezingin the UT and tropopause region is expected to occur insubmicron droplets.[6] In the present study we first show that the phase of icethat will form in the UT and tropopause is stronglydependent on the type of solute. Second, we also show thatthe amount of cubic ice formed in the aqueous solutiondroplets at temperatures below 200 K is independent ofdroplet size. In addition, we discuss the atmospheric impli-cations of these results and outline the possible implicationsfor climate and stratospheric water vapor.[7] We have focused this study on solutions of(NH4)3H(SO4)2/H2O (ammonium to sulfate ratios, ASR, =1.5) and NH4HSO4/H2O (ASR = 1.0) because initial testsshowed that they exhibit strongly contrasting behaviorand also because these compositions are relevant for theUT and tropopause region. These solutions are referred toas LET and AHS for the remainder of this paper;indicating that the overall stoichiometry of the solute inGEOPHYSICAL RESEARCH LETTERS, VOL. 34, L16810, doi:10.1029/2007GL030471, 2007ClickHereforFullArticle1Department of Chemistry, University of British Columbia, Vancouver,British Columbia, Canada.2Now at School of Chemistry, University of Leeds, Leeds, U.K.Copyright 2007 by the American Geophysical Union.0094-8276/07/2007GL030471$05.00L16810 1of5the droplets corresponds to letovicite and ammoniumbisulfate, respectively.2. Experiment[8] The experimental technique has been described pre-viously and will only be briefly summarized here [Murrayand Bertram, 2006; Murray et al., 2005]. In these experi-ments aqueous solution droplets (volume median diametersbetween 2 and 20 mm with geometric standard deviationsbetween 1.3 and 1.8) were suspended in an oil matrix, byemulsification, and the crystalline phases that formed whenthe droplets froze were monitored using X-ray diffraction.The temperatures at which ice crystallized in the dropletsas well as the melting temperatures of all the observedphases were also determined using X-ray diffraction as thedroplets were either cooled or warmed. The ice meltingtemperatures were typically within 1.5 K of those predictedby the Aerosol Inorganic Model [Clegg et al., 1998]. Themeasured mean freezing temperatures for AHS were typ-ically within 3 K of the previous measurements of thefreezing of droplets in emulsions [Koop et al., 1999]. Forboth AHS and LET the freezing temperatures were within5 K of a parameterization relating water activity to thehomogeneous freezing temperature [Koop et al., 2000].[9] In a typical experiment emulsified droplets werecooled at a rate of 10 K minC01from room temperature to173 K, while monitoring a pertinent range of diffractionangles to determine the temperature range over which thedroplets froze. When at 173 K (or 163 K in a few caseswhere the freezing temperature was particularly low) thefull diffraction pattern between 19 and 50C176 was measured inorder to determine the phases that had crystallized. 173 Kwas thought to be sufficiently cold that no further changesoccur in the droplets during the time it took to acquire anX-ray diffraction pattern with a reasonable signal-to-noiseratio (30–40 minutes).3. Results[10] Examples of the diffraction patterns of frozen LET,and AHS solution droplets, which contain Bragg peaks fromboth ice and crystalline solute phases, are illustrated inFigure 1. The peaks exclusive to ice Ihhave been labeled‘‘h’’; the peaks common to both ice Icand ice Ihhave beenlabeled ‘‘h + c’’; and the peaks due to the crystalline solutephases are labeled ‘‘S’’. When ice forms in solution dropletsit is well known that the majority of the solute ions ormolecules are not typically incorporated in the ice structureand are instead rejected to form liquid brine, which maycrystallize itself [Pruppacher and Klett, 1997]. The identi-fication of the crystalline solute phases will be addressed indetail in a separate publication; but briefly, the solute phasesthat crystallized in these experiments were identified fromthe peaks in the diffraction patterns and also meltingtemperatures. The solute phases that crystallized after thefreezing of ice were the mineral letovicite in LET dropletsand sulfuric acid tetrahydrate (SAT) as well as letovicite inAHS solution droplets.[11] There is a great deal of variability in the diffractionpatterns depending on the solute and also on the concen-tration of the solution droplets. In some cases the solutiondroplets froze dominantly to ice Ihwith no indication thatthe solute crystallized. Whereas, more concentrated solutiondroplets have diffraction patterns that lack several peaksexclusive to ice Ih. This indicates that these frozen dropletsdid not contain any bulk ice Ihand also the dominantfreezing product was ice Ic. However, these cubic patternsFigure 1. Diffraction patterns of frozen (a) AHS and (b) LET droplets. These patterns were measured after the dropletshad been cooled at a rate of 10 K minC01to 173 K (or 163 K in the case of the 36.2 wt% AHS droplets). Bragg peaksassociated with ice Ihare labeled ‘‘h’’, while those common to both ice Ihand ice Icare labeled ‘‘h + c’’. Peaks associatedwith the crystalline solute phase are labeled ‘‘S’’ and those due to the cell construction materials and the aluminum base arelabeled ‘‘Cell’’ and ‘‘Al’’, respectively.L16810 MURRAY AND BERTRAM: STRONG DEPENDENCE OF CUBIC ICE FORMATION L168102of5do have a strong peak at the position of the ice Ih(100)reflection at 23C176. In addition, the region between 2q = 22.5C176and 26.5C176 is raised above the background. These featuresindicate that the cubic ice contains ‘hexagonal like’ stackingfaults; in fact, stacking faults are thought to be inherent inice Ic[Kohl et al., 2000; Kuhs et al., 2004; Murray et al.,2005]. The presence of stacking faults in the ice structureprecludes the use of a standard Rietveld refinement of ourpowder patterns. Instead we have used alternative methodsto determine the fraction of ice that is cubic (see below).[12] There is also a great deal of variability in the amountof solute phase that crystallizes in the droplets. In mediumconcentration solutions the solute phase crystallizes, butin the most concentrated solutions (41.58 wt % LET and36.17 wt % AHS) the solute does not crystallize. The reasonfor this is likely because the aqueous brine that formed inthe concentrated solution droplets after the precipitation ofice is very viscous at low temperatures, thus drasticallydecreasing the crystallization rate.[13] In order to provide a measure of the amount of iceIhand Icin the frozen droplets, we determined ratios ofintensities of exclusive ice Ihpeaks to intensities of peakscommon to both ice Ihand Ic. This is the same procedurewe used in our previous publications to provide a measureof the amount of cubic ice in crystalline droplets [Murrayand Bertram, 2006; Murray et al., 2005]. Specifically wedetermined the intensity ratios I44/I40, I34/I40, and I44/I47(where I44and I34are the intensities of the exclusivehexagonal peaks at 2q C25 43.6C176 and 33.5C176; and I40and I47are peak intensities common to cubic and hexagonal iceat 2q C25 39.9C176 and 47.3C176). Ratios of I44/I40= 0.82 ± 0.03,I34/I40= 0.53 ± 0.03, I44/I47= 2.0 ± 0.1 indicate pure iceIh and ratios of zero indicates stacking faulty ice Ic. Theratios for pure hexagonal ice were calculated from diffrac-tion patterns of frozen pure water droplets which wereannealed at 268 K for 10 minutes. These ratios are in goodagreement with those reported for hexagonal ice previously[see Murray and Bertram, 2006, and references therein]. Ifthe peaks used in the above calculations partially over-lapped with peaks due to crystalline solute phases, we useda peak fitting procedure to separate the overlapping peaksinto their components prior to calculating integrated inten-sities. This procedure consisted of fitting the partiallyoverlapping peaks to Gaussian functions by regression afterbackground subtraction.[14] Shown in Figure 2 is the ratio I44/I40as a function ofthe homogeneous freezing temperature. In the auxiliarymaterial1we included plots of the ratio of I34/I40andI44/I47as a function of freezing temperature. The sametrend was observed in all three cases, as expected. The datain these plots are split into three droplet size bins. Sizes referto the volume median diameter which was determined usingan optical microscope.4. Discussion and Conclusions[15] Inspection of the sigmoidal fit through the 5–10 mmsize bin, shown in Figure 2, reveals that for AHS there is nosignificant size dependence for the entire temperature rangeinvestigated. For LET solution compositions, there is nosize dependence for temperatures less than C24200 K, whichis the region most relevant for the tropical tropopause andalso the region where the LET droplets dominantly formedcubic ice with stacking faults.[16] At higher freezing temperatures there is evidence ofa size dependence in the LET data, with larger dropletsfreezing to more ice Ic; an opposite trend to that observed inpure water droplets [Murray and Bertram, 2006]. The trendobserved previously for pure water is due to heating of thedroplets during crystallization. However, as discussed be-low, this is most likely not important for concentratedsolution droplets; and indeed, one would expect an oppositesize dependence if heating were important. Instead the size1Auxiliary materials are available in the HTML. doi:10.1029/2007GL030471.Figure 2. The intensity ratios I44/I40plotted as a functionof mean droplet freezing temperature (where I44is theintensities of the exclusive hexagonal peaks at 2q C25 43.6C176and I40is the peak intensity common to cubic andhexagonal ice at 2q C25 39.9C176). The data are grouped intothree size bins, 2–5 mm, 5–10 mm and 10–20 mm. Theshaded area indicates the range of temperatures relevant forthe UT and tropopause region [Zhou et al., 2004]. The solidline is a fit to the 5–10 mm size bin. The dashed linesindicate the 95% prediction bands.L16810 MURRAY AND BERTRAM: STRONG DEPENDENCE OF CUBIC ICE FORMATION L168103of5dependence for the LET data is most likely related to theamount of the solute phase that crystallized in the droplets.Initial results show that for this freezing temperature range(220 K–200 K) the amount of cubic ice that crystallizescorrelates with the relative amount of solute phase thatcrystallized in the LET system. This will be the focus of afuture study and is beyond the scope of the current manu-script. Further experiments are required to probe the com-plex processes taking place during crystallization.[17] One factor that can determine the final proportion ofice Icin frozen droplets is the relative rates of heatdissipation (L) and heat production (P) in the individualparticles during the freezing process. If a particle heats upsufficiently during freezing, ice Icwill be annealed to ice Ih.In our previous work we argued that pure water droplets(volume median diameter >5 mm) warmed up significantlyduring the freezing process, which results in ice Icannealingto ice Ih[Murray and Bertram, 2006]. In contrast to purewater, when concentrated solution droplets freeze homoge-neously, either in our emulsions experiments or in theatmosphere, L C29 P[Murray et al., 2005]. This is becausethe crystal growth rate, and therefore P, is very slow in low-temperature viscous liquids. For example, separate experi-ments using optical microscopy show that a 40 wt %(NH4)2SO4/H2O droplet (10 mm in diameter) takes approx-imately one third of a second to freeze at 200 K. Concen-trated solution droplets will experience no appreciableheating when they freeze (at C20 200 K) based on this resultand simple heat transfer calculations [Murray et al., 2005].Also, as mentioned above, if heating was important for thetemperature range we explored, then the amount of cubicice observed in our experiments should decrease as theparticle size was increased. Since we did not observe thistrend, we argue that heating was not important for thetemperature range explored. This is an important conclusionbecause if heating was important we would need to take intoaccount the fact that the thermal conductivity of oil isapproximately a factor of 10 greater than the thermalconductivity of air when extrapolating our laboratory resultsto the atmosphere.[18] Perhaps the most important result illustrated inFigure 2 is that the temperature below which cubic iceforms is strongly dependent on the solute type. Forexample, in LET droplets, the intensity ratios I44/I40is lessthan 0.2 at freezing temperatures below 200 ± 1 K (based onthe fit to the freezing data), whereas for AHS droplets avalue of 0.2 is not reached until below 183 ± 1 K.Uncertainties are based on the 95% confidence limit ofthe fit to the 5–10 mm size bin in Figure 2 (dashed lines).This shift of approximately 17 K may have importantimplications for the atmosphere. A similar shift wasobserved for all three intensity ratio plots (see the auxiliarymaterial).[19] In the UT and tropopause region, the lower climato-logical temperature limit is approximately 188 K. Thislower limit is indicated in Figure 2 by the shaded region.Furthermore, the temperature in the topical tropopauseregion is typically between 188 and 200 K [Zhou et al.,2004]. The measurements of ice phase in LET and AHSsolution droplets of varying concentration presented hereindicate that the phase of ice which forms in the UT andtropopause region will strongly depend on the ammoniumto sulfate ratio (ASR) of the sulfate aerosols from which iceclouds form. Our results show that droplets with ASR = 1.5may freeze dominantly to ice Icover a range of temperaturesrelevant for the UT and tropopause. However, droplets withASR = 1.0 do not freeze dominantly to ice Icundertemperatures relevant for the UT and tropopause region.This finding leads us to pose two fundamental questions:firstly, what is the composition of aerosols in the UT andtropopause region (i.e., is the composition closer to AHS orLET)? Secondly, has the composition of aerosols in theseregions changed due to man’s activities?[20] Unfortunately, there are very few quantitative mea-surements of UT aerosol composition. We now brieflyreview the few measurements that have been made. Dibbet al. [2000] found that aerosols collected on filters ataltitudes higher than 10 km over the North Atlantic duringautumn had a composition that was close to ammoniumsulfate. Field studies of aerosols in the Asian continentaloutflow found an average ASR of close to one (AHS) [Dibbet al., 1996]. In a field experiment to characterize aerosolsabove the Pacific (between 7–13 km altitude) duringSeptember and October Dibb et al. [1996] found thatparticles in the Northern hemisphere had an average ASRof close to the composition of LET (1.5), whereas in theSouthern hemisphere they where more acidic with an ASRof one or less. In contrast, Huebert et al. [1998] found nosignificant hemispherical dependence of ASR in the freetroposphere and found a median ASR of 1.2. Three-dimen-sional global models predict that aerosols in the UT are lessacidic in the northern hemisphere than in the southernhemisphere. In part, this is likely due to the proximity toanthropogenic sources of NH3[Adams et al., 1999; Martinet al., 2004].[21] In summary, the available measurements and modelssuggest that the ASR of UT (and tropopause) aerosols ishighly variable and do include the solute types (AHS andLET) investigated in this study. While the available meas-urements indicate that the ASR will favor the formation ofcubic ice in some situations (i.e., where T < 200 K and theASR = 1.5), our knowledge of ASR in the UT is notsufficient to confidently predict when and where the for-mation of cubic ice will be favored. Also, the presence oforganics and nitrate in the aerosol particles may influencethe amount of cubic ice that may form. Further work isneeded to better quantify the composition of UT andtropopause aerosols and in addition laboratory studies onthe formation of cubic ice in solution droplets containingnitrates and organics would be beneficial.[22] As for the second question posed above, emissionsof both SO2and NH3(sources of sulfate and ammonium)have increased significantly since pre-industrial times.Penner et al. [2001] summarize the natural and anthropo-genic emissions of NH3,SO2and DMS (dimethylsulphide)in the northern and southern hemispheres [see Penner et al.,2001, Table 5.2]. Natural emissions of NH3andS-containingspecies (SO2and DMS) are similar in the northern andsouthern hemispheres, while the majority of anthropogenicemissions are in the northern hemisphere. The main anthro-pogenic source of NH3is from agriculture and livestock andthat of SO2is the combustion of fossil fuels. According tothese figures, anthropogenic activity has increased the totalglobal emissions of NH3and S by approximately 400% andL16810 MURRAY AND BERTRAM: STRONG DEPENDENCE OF CUBIC ICE FORMATION L168104of5200% (in terms of moles of N and S), respectively. TheimpactofanthropogenicemissionsonthecompositionofUTaerosols is difficult to predict because quantifying the trans-port of these species is non-trivial. However, the increasedemissions of NH3relative to S containing gases mightsuggest that UTaerosols may have become more neutralized(i.e., less acidic). If this is the case, then our results suggestthat the probability of a cloud freezing to cubic ice may haveincreased due to agricultural and livestock NH3emissions.Hence, agricultural activity may have indirectly affectedclimate and stratospheric ozone by modifying the frequencyof cubic ice clouds in the UT and tropopause region. Asmentioned in the introduction the formation of cubic iceclouds may impact climate, water vapor distributions andstratospheric ozone by several mechanisms.[23] Acknowledgments. The authors thank A. Lam and B. Patrick forassistance with X-ray diffraction measurements and interpretation of thediffraction patterns. We also thank D. Murphy, D. Cziczo and P. Adams forhelpful discussions on the composition of UT aerosols. This work wasfunded by the Natural Science and Engineering Research Council ofCanada, NSERC, the Canadian Foundation for Climate and AtmosphericSciences, CFCAS, and the Canada Foundation for Innovation, CFI. BJMacknowledges the Natural Environmental Research Council, NERC, for afellowship held at the School of Chemistry (University of Leeds) whichcommenced September 2006.ReferencesAbbatt, J. P. D. (2003), Interactions of atmospheric trace gases with icesurfaces: Adsorption and reaction, Chem. Rev., 103, 4783–4800.Adams, P. J., J. H. Seinfeld, and D. M. Koch (1999), Global concentrationsof tropospheric sulfate, nitrate, and ammonium aerosol simulated in ageneral circulation model, J. Geophys. Res., 104, 13,791–13,823.Behr, P., A. Terziyski, and R. Zellner (2006), Acetone adsorption on icesurfaces in the temperature range T = 190–220 K: Evidence for agingeffects due to crystallographic changes of the adsorption sites, J. Phys.Chem. A, 110, 8098–8107.Clegg, S. L., P. Brimblecombe, and A. S. Wexler (1998), Thermodynamicmodel of the system H+-NH4+-SO42C0-NO3C0-H2O at tropospheric tempera-tures, J. Phys. Chem. A, 102, 2137–2154.DeMott, P. J. (2002), Laboratory studies of cirrus cloud processes, in Cir-rus, edited by D. K. Lynch et al., pp. 102–135, Oxford Univ. Press,Oxford, U. K.Dibb, J. E., R. W. Talbot, K. I. Klemm, G. L. Gregory, H. B. Singh, J. D.Bradshaw, and S. T. Sandholm (1996), Asian influence over the westernNorth Pacific during the fall season: Inferences from lead 210, solubleionic species and ozone, J. Geophys. Res., 101, 1779–1792.Dibb, J. E., R. W. Talbot, and E. M. Scheuer (2000), Composition anddistribution of aerosols over the North Atlantic during the SubsonicAssessment Ozone and Nitrogen Oxide Experiment (SONEX), J. Geo-phys. Res., 105, 3709–3717.Huebert, B. J., S. G. Howell, L. Zhuang, J. A. Heath, M. R. Litchy, D. J.Wylie, J. L. Kreidler-Moss, S. Coppicus, and J. E. Pfeiffer (1998), Filterand impactor measurements of anions and cations during the First Aero-sol Characterization Experiment (ACE 1), J. Geophys. Res., 103,16,493–16,509.Jensen, E., and L. Pfister (2005), Implications of persistent ice supersatura-tion in cold cirrus for stratospheric water vapor, Geophys. Res. Lett., 32,L01808, doi:10.1029/2004GL021125.Kohl, I., E. Mayer, and A. Hallbrucker (2000), The glassy water-cubic icesystem: A comparative study by X-ray diffraction and differential scan-ning calorimetry, Phys. Chem. Chem. Phys., 2, 1579–1586.Koop, T., A. K. Bertram, L. T. Molina, and M. J. Molina (1999), Phasetransitions in aqueous NH4HSO4solutions, J. Phys. Chem. A, 103,9042–9048.Koop, T., B. P. Luo, A. Tsias, and T. Peter (2000), Water activity as thedeterminant for homogeneous ice nucleation in aqueous solutions, Nature,406, 611–614.Kuhs, W. F., G. Genov, D. K. Staykova, and T. Hansen (2004), Ice perfec-tion and onset of anomalous preservation of gas hydrates, Phys. Chem.Chem. Phys., 6, 4917–4920.Martin, S. T., H. M. Hung, R. J. Park, D. J. Jacob, R. J. D. Spurr, K. V.Chance, and M. Chin (2004), Effects of the physical state of troposphericammonium-sulfate-nitrate particles on global aerosol direct radiative for-cing, Atmos. Chem. Phys., 4, 183–214.Murphy, D. M. (2003), Dehydration in cold clouds is enhanced by a transi-tion from cubic to hexagonal ice, Geophys. Res. Lett., 30(23), 2230,doi:10.1029/2003GL018566.Murray, B. J., and A. K. Bertram (2006), Formation and stability of cubicice in water droplets, Phys. Chem. Chem. Phys., 8, 186–192.Murray, B. J., D. A. Knopf, and A. K. Bertram (2005), The formation ofcubic ice under conditions relevant to Earth’s atmosphere, Nature, 434,202–205.Penner, J. E., et al. (2001), Aerosols, their direct and indirect effects, inClimate Change 2001: The Scientific Basis. Contributions of WorkingGroup I to the Third Assessment Report of the Intergovernmental Panelon Climate Change, edited by B. Nyenzi and J. Prespero, pp. 291–348,Cambridge Univ. Press, New York.Pruppacher, H. R., and J. D. Klett (1997), Microphysics of Clouds andPrecipitation, Kluwer, Dordrecht, Netherlands.Shilling, J. E., M. A. Tolbert, O. B. Toon, E. J. Jensen, B. J. Murray, andA. K. Bertram (2006), Measurements of the vapor pressure of cubic iceand their implications for atmospheric ice clouds, Geophys. Res. Lett., 33,L17801, doi:10.1029/2006GL026671.Zhou, X. L., M. A. Geller, and M. H. Zhang (2004), Temperature fields inthe tropical tropopause transition layer, J. Clim., 17, 2901–2908.C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0A. K. Bertram, Department of Chemistry, University of British Columbia,2036 Main Mall, Vancouver, BC, Canada V6T 1Z1. (bertram@chem.ubc.ca)B. J. Murray, School of Chemistry, University of Leeds, WoodhouseLane, Leeds LS2 9JT, UK. (b.j.murray@leeds.ac.uk)L16810 MURRAY AND BERTRAM: STRONG DEPENDENCE OF CUBIC ICE FORMATION L168105of5


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