UBC Faculty Research and Publications

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


52383-Bertram_2007GL030471.pdf [ 311.58kB ]
JSON: 52383-1.0041858.json
JSON-LD: 52383-1.0041858-ld.json
RDF/XML (Pretty): 52383-1.0041858-rdf.xml
RDF/JSON: 52383-1.0041858-rdf.json
Turtle: 52383-1.0041858-turtle.txt
N-Triples: 52383-1.0041858-rdf-ntriples.txt
Original Record: 52383-1.0041858-source.json
Full Text

Full Text

Click Here  GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L16810, doi:10.1029/2007GL030471, 2007  for  Full Article  Strong dependence of cubic ice formation on droplet ammonium to sulfate ratio Benjamin J. Murray1,2 and Allan K. Bertram1 Received 27 April 2007; revised 31 May 2007; accepted 28 June 2007; published 23 August 2007.  [1] We show that the phase of ice that crystallizes in solution droplets, under conditions relevant for the upper troposphere (UT) and tropopause region (typically >188 K), is strongly dependent on the ammonium to sulfate ratio (ASR) of the solute. Droplets of aqueous (NH4)3H(SO4)2 (ASR = 1.5) freeze dominantly to cubic ice over a range of temperatures relevant for the UT and tropopause; whereas aqueous NH4HSO4 (ASR = 1.0) droplets do not freeze dominantly to ice Ic at temperatures relevant for the UT and tropopause region. We also show that the amount of cubic ice formed in the aqueous solution droplets at temperatures below 200 K is independent of droplet size, whereas a size dependence was observed at higher temperatures. The implications of these results for the phase of ice that forms in upper tropospheric ice clouds and the potential impact on climate, water vapor, and ozone are briefly discussed. Citation: Murray, B. J., and A. K. Bertram (2007), Strong dependence of cubic ice formation on droplet ammonium to sulfate 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 the Earth’s climate by scattering and absorbing radiation. In addition, they influence the distribution of water vapor in the troposphere as well as the amount that enters the stratosphere, where changes in humidity may have important consequences for polar stratospheric ozone [Jensen and Pfister, 2005]. Ice clouds in the UT and tropopause region, including cirrus and cirrostratus, influence the chemistry of the atmosphere by providing a surface on which heterogeneous chemical reactions can occur [Abbatt, 2003]. Despite the potential impact of ice clouds on the planet’s atmosphere and climate, many important details regarding their formation mechanisms and microphysics remain poorly understood [DeMott, 2002; Penner et al., 2001]. [3] A significant mechanism of ice cloud formation in the UT and tropopause region is thought to be homogeneous freezing of submicron aqueous droplets [DeMott, 2002]. Recently it was shown that the metastable cubic crystalline phase of ice (ice Ic) was produced when a range of solution droplets froze homogeneously under conditions that were  1 Department of Chemistry, University of British Columbia, Vancouver, British Columbia, Canada. 2 Now at School of Chemistry, University of Leeds, Leeds, U.K.  Copyright 2007 by the American Geophysical Union. 0094-8276/07/2007GL030471$05.00  relevant for the UT and tropopause [Murray et al., 2005]. Previous to this work, it was often assumed that only the stable hexagonal phase (ice Ih) would form under conditions relevant for the UT and tropopause [Pruppacher and Klett, 1997]. [4] Recent laboratory measurements have shown clouds composed of ice Ic will have a saturation vapor pressure 11 ± 3% larger than that of a cloud composed of ice Ih [Shilling et al., 2006]. Hence, the formation of cubic ice in the UT and tropopause region may have some important implications: Murphy [2003] has shown that the difference in vapor pressure between ice Ic and ice Ih may strongly influence cloud properties and lifetimes through a process analogous to the Bergeron-Findeisen process in which hexagonal ice crystals grow at the expense of metastable cubic ice crystals. Jensen and Pfister [2005] examined the impact of persistent high ice supersaturations in cold cirrus clouds. They found that transport of water into the stratosphere is enhanced and cloud properties were altered. Also, a recent laboratory investigation revealed that cubic and hexagonal ice have different heterogeneous chemistries [Behr et al., 2006], which may have important implications for the processing of gas phase species by ice clouds. [5] As mentioned, recently it was shown that ice Ic was produced when a range of solution droplets froze homogeneously under conditions that are relevant for the Earth’s atmosphere [Murray et al., 2005]. However, the effect of the solute type on the amount of Ic produced was not studied in detail. Moreover, the effect of droplet size on the amount of Ic formed in aqueous solution droplets was not explored. The size dependence is important for extrapolating laboratory data to the atmosphere, since laboratory measurements were performed on supermicron droplets, whereas freezing in the UT and tropopause region is expected to occur in submicron droplets. [6] In the present study we first show that the phase of ice that will form in the UT and tropopause is strongly dependent on the type of solute. Second, we also show that the amount of cubic ice formed in the aqueous solution droplets at temperatures below 200 K is independent of droplet size. In addition, we discuss the atmospheric implications of these results and outline the possible implications for 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 tests showed that they exhibit strongly contrasting behavior and also because these compositions are relevant for the UT and tropopause region. These solutions are referred to as LET and AHS for the remainder of this paper; indicating that the overall stoichiometry of the solute in  L16810  1 of 5  L16810  MURRAY AND BERTRAM: STRONG DEPENDENCE OF CUBIC ICE FORMATION  L16810  Figure 1. Diffraction patterns of frozen (a) AHS and (b) LET droplets. These patterns were measured after the droplets had been cooled at a rate of 10 K minÀ1 to 173 K (or 163 K in the case of the 36.2 wt% AHS droplets). Bragg peaks associated with ice Ih are labeled ‘‘h’’, while those common to both ice Ih and ice Ic are labeled ‘‘h + c’’. Peaks associated with the crystalline solute phase are labeled ‘‘S’’ and those due to the cell construction materials and the aluminum base are labeled ‘‘Cell’’ and ‘‘Al’’, respectively. the droplets corresponds to letovicite and ammonium bisulfate, respectively.  occur in the droplets during the time it took to acquire an X-ray diffraction pattern with a reasonable signal-to-noise ratio (30 – 40 minutes).  2. Experiment [8] The experimental technique has been described previously and will only be briefly summarized here [Murray and Bertram, 2006; Murray et al., 2005]. In these experiments aqueous solution droplets (volume median diameters between 2 and 20 mm with geometric standard deviations between 1.3 and 1.8) were suspended in an oil matrix, by emulsification, and the crystalline phases that formed when the droplets froze were monitored using X-ray diffraction. The temperatures at which ice crystallized in the droplets as well as the melting temperatures of all the observed phases were also determined using X-ray diffraction as the droplets were either cooled or warmed. The ice melting temperatures were typically within 1.5 K of those predicted by the Aerosol Inorganic Model [Clegg et al., 1998]. The measured mean freezing temperatures for AHS were typically within 3 K of the previous measurements of the freezing of droplets in emulsions [Koop et al., 1999]. For both AHS and LET the freezing temperatures were within 5 K of a parameterization relating water activity to the homogeneous freezing temperature [Koop et al., 2000]. [9] In a typical experiment emulsified droplets were cooled at a rate of 10 K minÀ1 from room temperature to 173 K, while monitoring a pertinent range of diffraction angles to determine the temperature range over which the droplets froze. When at 173 K (or 163 K in a few cases where the freezing temperature was particularly low) the full diffraction pattern between 19 and 50° was measured in order to determine the phases that had crystallized. 173 K was thought to be sufficiently cold that no further changes  3. Results [10] Examples of the diffraction patterns of frozen LET, and AHS solution droplets, which contain Bragg peaks from both ice and crystalline solute phases, are illustrated in Figure 1. The peaks exclusive to ice Ih have been labeled ‘‘h’’; the peaks common to both ice Ic and ice Ih have been labeled ‘‘h + c’’; and the peaks due to the crystalline solute phases are labeled ‘‘S’’. When ice forms in solution droplets it is well known that the majority of the solute ions or molecules are not typically incorporated in the ice structure and are instead rejected to form liquid brine, which may crystallize itself [Pruppacher and Klett, 1997]. The identification of the crystalline solute phases will be addressed in detail in a separate publication; but briefly, the solute phases that crystallized in these experiments were identified from the peaks in the diffraction patterns and also melting temperatures. The solute phases that crystallized after the freezing of ice were the mineral letovicite in LET droplets and sulfuric acid tetrahydrate (SAT) as well as letovicite in AHS solution droplets. [11] There is a great deal of variability in the diffraction patterns depending on the solute and also on the concentration of the solution droplets. In some cases the solution droplets froze dominantly to ice Ih with no indication that the solute crystallized. Whereas, more concentrated solution droplets have diffraction patterns that lack several peaks exclusive to ice Ih. This indicates that these frozen droplets did not contain any bulk ice Ih and also the dominant freezing product was ice Ic. However, these cubic patterns  2 of 5  L16810  MURRAY AND BERTRAM: STRONG DEPENDENCE OF CUBIC ICE FORMATION  do have a strong peak at the position of the ice Ih (100) reflection at 23°. In addition, the region between 2q = 22.5° and 26.5° is raised above the background. These features indicate that the cubic ice contains ‘hexagonal like’ stacking faults; in fact, stacking faults are thought to be inherent in ice Ic [Kohl et al., 2000; Kuhs et al., 2004; Murray et al., 2005]. The presence of stacking faults in the ice structure precludes the use of a standard Rietveld refinement of our powder patterns. Instead we have used alternative methods to determine the fraction of ice that is cubic (see below). [12] There is also a great deal of variability in the amount of solute phase that crystallizes in the droplets. In medium concentration solutions the solute phase crystallizes, but in the most concentrated solutions (41.58 wt % LET and 36.17 wt % AHS) the solute does not crystallize. The reason for this is likely because the aqueous brine that formed in the concentrated solution droplets after the precipitation of ice is very viscous at low temperatures, thus drastically decreasing the crystallization rate. [13] In order to provide a measure of the amount of ice Ih and Ic in the frozen droplets, we determined ratios of intensities of exclusive ice Ih peaks to intensities of peaks common to both ice Ih and Ic. This is the same procedure we used in our previous publications to provide a measure of the amount of cubic ice in crystalline droplets [Murray and Bertram, 2006; Murray et al., 2005]. Specifically we determined the intensity ratios I44/I40, I34/I40, and I44/I47 (where I44 and I34 are the intensities of the exclusive hexagonal peaks at 2q % 43.6° and 33.5°; and I40 and I47 are peak intensities common to cubic and hexagonal ice at 2q % 39.9° and 47.3°). Ratios of I44/I40 = 0.82 ± 0.03, I34/I40 = 0.53 ± 0.03, I44/I47 = 2.0 ± 0.1 indicate pure ice Ih and ratios of zero indicates stacking faulty ice Ic. The ratios for pure hexagonal ice were calculated from diffraction patterns of frozen pure water droplets which were annealed at 268 K for 10 minutes. These ratios are in good agreement with those reported for hexagonal ice previously [see Murray and Bertram, 2006, and references therein]. If the peaks used in the above calculations partially overlapped with peaks due to crystalline solute phases, we used a peak fitting procedure to separate the overlapping peaks into their components prior to calculating integrated intensities. This procedure consisted of fitting the partially overlapping peaks to Gaussian functions by regression after background subtraction. [14] Shown in Figure 2 is the ratio I44/I40 as a function of the homogeneous freezing temperature. In the auxiliary material1 we included plots of the ratio of I34/I40 and I44/I47 as a function of freezing temperature. The same trend was observed in all three cases, as expected. The data in these plots are split into three droplet size bins. Sizes refer to the volume median diameter which was determined using an optical microscope.  4. Discussion and Conclusions [15] Inspection of the sigmoidal fit through the 5 –10 mm size bin, shown in Figure 2, reveals that for AHS there is no significant size dependence for the entire temperature range 1 Auxiliary materials are available in the HTML. doi:10.1029/ 2007GL030471.  L16810  Figure 2. The intensity ratios I44/I40 plotted as a function of mean droplet freezing temperature (where I44 is the intensities of the exclusive hexagonal peaks at 2q % 43.6° and I40 is the peak intensity common to cubic and hexagonal ice at 2q % 39.9°). The data are grouped into three size bins, 2 – 5 mm, 5 –10 mm and 10– 20 mm. The shaded area indicates the range of temperatures relevant for the UT and tropopause region [Zhou et al., 2004]. The solid line is a fit to the 5 – 10 mm size bin. The dashed lines indicate the 95% prediction bands. investigated. For LET solution compositions, there is no size dependence for temperatures less than $200 K, which is the region most relevant for the tropical tropopause and also the region where the LET droplets dominantly formed cubic ice with stacking faults. [16] At higher freezing temperatures there is evidence of a size dependence in the LET data, with larger droplets freezing to more ice Ic; an opposite trend to that observed in pure water droplets [Murray and Bertram, 2006]. The trend observed previously for pure water is due to heating of the droplets during crystallization. However, as discussed below, this is most likely not important for concentrated solution droplets; and indeed, one would expect an opposite size dependence if heating were important. Instead the size  3 of 5  L16810  MURRAY AND BERTRAM: STRONG DEPENDENCE OF CUBIC ICE FORMATION  dependence for the LET data is most likely related to the amount 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 crystallizes correlates with the relative amount of solute phase that crystallized in the LET system. This will be the focus of a future study and is beyond the scope of the current manuscript. Further experiments are required to probe the complex processes taking place during crystallization. [17] One factor that can determine the final proportion of ice Ic in frozen droplets is the relative rates of heat dissipation (L) and heat production (P) in the individual particles during the freezing process. If a particle heats up sufficiently during freezing, ice Ic will be annealed to ice Ih. In our previous work we argued that pure water droplets (volume median diameter >5 mm) warmed up significantly during the freezing process, which results in ice Ic annealing to ice Ih [Murray and Bertram, 2006]. In contrast to pure water, when concentrated solution droplets freeze homogeneously, either in our emulsions experiments or in the atmosphere, L ) P [Murray et al., 2005]. This is because the crystal growth rate, and therefore P, is very slow in lowtemperature viscous liquids. For example, separate experiments using optical microscopy show that a 40 wt % (NH4)2SO4/H2O droplet (10 mm in diameter) takes approximately one third of a second to freeze at 200 K. Concentrated solution droplets will experience no appreciable heating when they freeze (at 200 K) based on this result and simple heat transfer calculations [Murray et al., 2005]. Also, as mentioned above, if heating was important for the temperature range we explored, then the amount of cubic ice observed in our experiments should decrease as the particle size was increased. Since we did not observe this trend, we argue that heating was not important for the temperature range explored. This is an important conclusion because if heating was important we would need to take into account the fact that the thermal conductivity of oil is approximately a factor of 10 greater than the thermal conductivity of air when extrapolating our laboratory results to the atmosphere. [18] Perhaps the most important result illustrated in Figure 2 is that the temperature below which cubic ice forms is strongly dependent on the solute type. For example, in LET droplets, the intensity ratios I44/I40 is less than 0.2 at freezing temperatures below 200 ± 1 K (based on the fit to the freezing data), whereas for AHS droplets a value of 0.2 is not reached until below 183 ± 1 K. Uncertainties are based on the 95% confidence limit of the fit to the 5– 10 mm size bin in Figure 2 (dashed lines). This shift of approximately 17 K may have important implications for the atmosphere. A similar shift was observed for all three intensity ratio plots (see the auxiliary material). [19] In the UT and tropopause region, the lower climatological temperature limit is approximately 188 K. This lower limit is indicated in Figure 2 by the shaded region. Furthermore, the temperature in the topical tropopause region is typically between 188 and 200 K [Zhou et al., 2004]. The measurements of ice phase in LET and AHS solution droplets of varying concentration presented here indicate that the phase of ice which forms in the UT and tropopause region will strongly depend on the ammonium  L16810  to sulfate ratio (ASR) of the sulfate aerosols from which ice clouds form. Our results show that droplets with ASR = 1.5 may freeze dominantly to ice Ic over a range of temperatures relevant for the UT and tropopause. However, droplets with ASR = 1.0 do not freeze dominantly to ice Ic under temperatures 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 and tropopause region (i.e., is the composition closer to AHS or LET)? Secondly, has the composition of aerosols in these regions changed due to man’s activities? [20] Unfortunately, there are very few quantitative measurements of UT aerosol composition. We now briefly review the few measurements that have been made. Dibb et al. [2000] found that aerosols collected on filters at altitudes higher than 10 km over the North Atlantic during autumn had a composition that was close to ammonium sulfate. Field studies of aerosols in the Asian continental outflow found an average ASR of close to one (AHS) [Dibb et al., 1996]. In a field experiment to characterize aerosols above the Pacific (between 7 – 13 km altitude) during September and October Dibb et al. [1996] found that particles in the Northern hemisphere had an average ASR of close to the composition of LET (1.5), whereas in the Southern hemisphere they where more acidic with an ASR of one or less. In contrast, Huebert et al. [1998] found no significant hemispherical dependence of ASR in the free troposphere and found a median ASR of 1.2. Three-dimensional global models predict that aerosols in the UT are less acidic in the northern hemisphere than in the southern hemisphere. In part, this is likely due to the proximity to anthropogenic sources of NH3 [Adams et al., 1999; Martin et al., 2004]. [21] In summary, the available measurements and models suggest that the ASR of UT (and tropopause) aerosols is highly variable and do include the solute types (AHS and LET) investigated in this study. While the available measurements indicate that the ASR will favor the formation of cubic ice in some situations (i.e., where T < 200 K and the ASR = 1.5), our knowledge of ASR in the UT is not sufficient to confidently predict when and where the formation of cubic ice will be favored. Also, the presence of organics and nitrate in the aerosol particles may influence the amount of cubic ice that may form. Further work is needed to better quantify the composition of UT and tropopause aerosols and in addition laboratory studies on the formation of cubic ice in solution droplets containing nitrates and organics would be beneficial. [22] As for the second question posed above, emissions of both SO2 and NH3 (sources of sulfate and ammonium) have increased significantly since pre-industrial times. Penner et al. [2001] summarize the natural and anthropogenic emissions of NH3, SO2 and DMS (dimethylsulphide) in the northern and southern hemispheres [see Penner et al., 2001, Table 5.2]. Natural emissions of NH3 and S-containing species (SO2 and DMS) are similar in the northern and southern hemispheres, while the majority of anthropogenic emissions are in the northern hemisphere. The main anthropogenic source of NH3 is from agriculture and livestock and that of SO2 is the combustion of fossil fuels. According to these figures, anthropogenic activity has increased the total global emissions of NH3 and S by approximately 400% and  4 of 5  L16810  MURRAY AND BERTRAM: STRONG DEPENDENCE OF CUBIC ICE FORMATION  200% (in terms of moles of N and S), respectively. The impact of anthropogenic emissions on the composition of UT aerosols is difficult to predict because quantifying the transport of these species is non-trivial. However, the increased emissions of NH3 relative to S containing gases might suggest that UT aerosols may have become more neutralized (i.e., less acidic). If this is the case, then our results suggest that the probability of a cloud freezing to cubic ice may have increased due to agricultural and livestock NH3 emissions. Hence, agricultural activity may have indirectly affected climate and stratospheric ozone by modifying the frequency of cubic ice clouds in the UT and tropopause region. As mentioned in the introduction the formation of cubic ice clouds may impact climate, water vapor distributions and stratospheric ozone by several mechanisms. [23] Acknowledgments. The authors thank A. Lam and B. Patrick for assistance with X-ray diffraction measurements and interpretation of the diffraction patterns. We also thank D. Murphy, D. Cziczo and P. Adams for helpful discussions on the composition of UT aerosols. This work was funded by the Natural Science and Engineering Research Council of Canada, NSERC, the Canadian Foundation for Climate and Atmospheric Sciences, CFCAS, and the Canada Foundation for Innovation, CFI. BJM acknowledges the Natural Environmental Research Council, NERC, for a fellowship held at the School of Chemistry (University of Leeds) which commenced September 2006.  References Abbatt, J. P. D. (2003), Interactions of atmospheric trace gases with ice surfaces: Adsorption and reaction, Chem. Rev., 103, 4783 – 4800. Adams, P. J., J. H. Seinfeld, and D. M. Koch (1999), Global concentrations of tropospheric sulfate, nitrate, and ammonium aerosol simulated in a general circulation model, J. Geophys. Res., 104, 13,791 – 13,823. Behr, P., A. Terziyski, and R. Zellner (2006), Acetone adsorption on ice surfaces in the temperature range T = 190 – 220 K: Evidence for aging effects 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), Thermodynamic À model of the system H+-NH+4 -SO2À 4 -NO3 -H2O at tropospheric temperatures, J. Phys. Chem. A, 102, 2137 – 2154. DeMott, P. J. (2002), Laboratory studies of cirrus cloud processes, in Cirrus, 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 western North Pacific during the fall season: Inferences from lead 210, soluble ionic species and ozone, J. Geophys. Res., 101, 1779 – 1792. Dibb, J. E., R. W. Talbot, and E. M. Scheuer (2000), Composition and distribution of aerosols over the North Atlantic during the Subsonic  L16810  Assessment Ozone and Nitrogen Oxide Experiment (SONEX), J. Geophys. 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), Filter and impactor measurements of anions and cations during the First Aerosol Characterization Experiment (ACE 1), J. Geophys. Res., 103, 16,493 – 16,509. Jensen, E., and L. Pfister (2005), Implications of persistent ice supersaturation 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 ice system: A comparative study by X-ray diffraction and differential scanning calorimetry, Phys. Chem. Chem. Phys., 2, 1579 – 1586. Koop, T., A. K. Bertram, L. T. Molina, and M. J. Molina (1999), Phase transitions in aqueous NH4HSO4 solutions, J. Phys. Chem. A, 103, 9042 – 9048. Koop, T., B. P. Luo, A. Tsias, and T. Peter (2000), Water activity as the determinant for homogeneous ice nucleation in aqueous solutions, Nature, 406, 611 – 614. Kuhs, W. F., G. Genov, D. K. Staykova, and T. Hansen (2004), Ice perfection 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 tropospheric ammonium-sulfate-nitrate particles on global aerosol direct radiative forcing, Atmos. Chem. Phys., 4, 183 – 214. Murphy, D. M. (2003), Dehydration in cold clouds is enhanced by a transition 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 cubic ice in water droplets, Phys. Chem. Chem. Phys., 8, 186 – 192. Murray, B. J., D. A. Knopf, and A. K. Bertram (2005), The formation of cubic ice under conditions relevant to Earth’s atmosphere, Nature, 434, 202 – 205. Penner, J. E., et al. (2001), Aerosols, their direct and indirect effects, in Climate Change 2001: The Scientific Basis. Contributions of Working Group I to the Third Assessment Report of the Intergovernmental Panel on 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 and Precipitation, Kluwer, Dordrecht, Netherlands. Shilling, J. E., M. A. Tolbert, O. B. Toon, E. J. Jensen, B. J. Murray, and A. K. Bertram (2006), Measurements of the vapor pressure of cubic ice and 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 in the tropical tropopause transition layer, J. Clim., 17, 2901 – 2908. ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ  A. 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, Woodhouse Lane, Leeds LS2 9JT, UK. (b.j.murray@leeds.ac.uk)  5 of 5  


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items