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<front>
<journal-meta>
<journal-id journal-id-type="publisher">ACP</journal-id>
<journal-title-group>
<journal-title>Atmospheric Chemistry and Physics</journal-title>
<abbrev-journal-title abbrev-type="publisher">ACP</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1680-7324</issn>
<publisher><publisher-name>Copernicus GmbH</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/acp-9-685-2009</article-id>
<title-group>
<article-title>Modelling of cirrus clouds – Part 1a: Model description and validation</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Spichtinger</surname>
<given-names>P.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Gierens</surname>
<given-names>K. M.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Institute for Atmospheric and Climate Science, ETH Zurich, 8092 Zurich, Switzerland</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Deutsches Zentrum für Luft- und Raumfahrt, Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany</addr-line>
</aff>
<pub-date pub-type="epub">
<day>28</day>
<month>01</month>
<year>2009</year>
</pub-date>
<volume>9</volume>
<issue>2</issue>
<fpage>685</fpage>
<lpage>706</lpage>
<permissions>
<license xlink:type="simple">
<license-p>This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</license-p>
</license>
</permissions>
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<abstract>
<p>A double-moment bulk microphysics scheme for modelling
cirrus clouds including explicit impact of aerosols on different
types of nucleation mechanism is described. Process rates are
formulated in terms of generalised moments of the underlying a
priori size distributions in order to allow simple switching
between various distribution types. The scheme has been implemented
into a simple box model and into the anelastic non-hydrostatic model
EULAG. The new microphysics is validated against simulations with
detailed microphysics for idealised process studies and for a well
documented case of arctic cirrostratus. Additionally, the formation
of ice crystals with realistic background aerosol concentration is
modelled and the effect of ambient pressure on homogeneous
nucleation is investigated in the box model.

&lt;br&gt;&lt;br&gt;
The model stands all tests and is thus suitable for
cloud-resolving simulations of cirrus clouds.</p>
</abstract>
<counts><page-count count="22"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple"> Barthazy, E. and Schefold, R.: Fall velocity of snowflakes of different riming degree and crystal types, Atmos. Res., 82, 391–398, 2006. </mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Bailey, M. and J. Hallet, 2004: Growth rates and habits of ice crystals between –20 and –70&amp;deg;C, J. Atmos. Sci., 61, 514–544. </mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Bunz, H., Benz, S., Gensch, I., and Krämer, M.: MAID: a model to simulate UT/LS aerosols and ice clouds, Environ. Res. Lett., 3, 035001, doi: 10.1088/1748-9326/3/3/035001, 2008. </mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Chen, T., Rossow, W. B., and Zhang, Y.: Radiative Effects of Cloud-Type Variations, J. Climate, 13, 264–286, 2000. </mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Chiruta, M. and Wang, P. K.: The capacitance of solid and hollow hexagonal ice columns, Geophys. Res. Lett., 32, L05803, doi:10.1029/2004GL021771, 2005. </mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Comstock, J., Ackerman, T. P., Turner, D. D.: Evidence of high ice supersaturation in cirrus clouds using ARM Raman lidar measurements, Geophys. Res. Lett., 31, L11106, doi:10.1029/2004GL019705, 2004. </mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple"> Emanuel, K.: Atmospheric convection. Oxford University Press, 580 pp., 1994. </mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Fusina, F., Spichtinger, P., and Lohmann, U.: The impact of ice supersaturated regions and thin cirrus on radiation in the mid latitudes, J. Geophys. Res., 112, D24S14, doi:10.1029/2007JD008449, 2007. </mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Gao, R. S., Popp, P.J., Fahey, D.W., et al.: Evidence that nitric acid increases relative humidity in low-temperature cirrus clouds, Science, 303, 516–520, 2004. </mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple"> Gayet, J.-F., Shcherbakov, V., Mannstein, H., Minikin, A., Schumann, U., Ström, J., Petzold, A., Ovarlez, J., and Immler, F.: Microphysical and optical properties of midlatitude cirrus clouds observed in the southern hemisphere during INCA, Q. J. Roy. Meteror. Soc., 132, 2719–2748, 2006. </mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Gettelman, A., Fetzer, E. J., Eldering, A., Irion, F. W.: The global distribution of supersaturation in the upper troposphere from the atmospheric infrared sounder, J. Climate, 19, 6089–6103, 2006. </mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple"> Gierens, K.: Numerical simulations of persistent contrails, J. Atmos. Sci., 53, 3333–3348, 1996. </mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple"> Gierens, K. M. and Ström, J.: A numerical study of aircraft wake induced ice cloud formation, J. Atmos. Sci. 55, 3253–3263, 1998. </mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Gierens, K., Schumann, U., Helten, M., Smit, H., and Marenco, A.: A distribution law for relative humidity in the upper troposphere and lower stratosphere derived from three years of MOZAIC measurements, Ann. Geophys., 17, 1218–1226, 1999. </mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple"> Gierens, K.: On the transition between heterogeneous and homogeneous freezing, Atmos. Chem. Phys., 3, 437–446, 2003. </mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple"> Gierens, K., Monier, M., and Gayet, J.-F.: The deposition coefficient and its role for cirrus clouds, J. Geophys. Res., 108, 4069, doi:10.1029/2001JD001558, 2003. </mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple"> Grabowski, W. and Smolarkiewicz, P.: A multiscale anelastic model for meteorological research, Mon. Weather Rev., 130, 939–956, 2002. </mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Haag, W., Kärcher, B., Schurath, U., Möhler, O., Stetzer, O., Schaefers, S., Schiller, C., and Krämer, M.: Numerical simulations of homogeneous freezing processes in the aerosol chamber AIDA, Atmos. Chem. Phys., 3, 195–210, 2003a. </mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Haag, W. and Kärcher, B., Ström, J., Minikin, A., Lohmann, U., Ovarlez, J., and Stohl, A.: Freezing thresholds and cirrus cloud formation mechanisms inferred from in situ measurements of relative humidity, Atmos. Chem. Phys., 3, 1791–1806, 2003b. </mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Haag, W. and Kärcher, B.: The impact of aerosols and gravity waves on cirrus clouds at midlatitudes, J. Geophys. Res., 109, D12202, doi:10.1029/2004JD00457, 2004. </mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple"> Hall, W. D. and Pruppacher, H. R.: The survival of ice particles falling from cirrus clouds in subsaturated air, J. Atmos. Sci., 33, 1995–2006, 1976. </mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple"> Harrington, J. Y., Meyers, M. P., Walko, R. L., and Cotton, W. R.: Parameterization of ice crystal conversion processes due to vapor deposition for mesoscale models using double-moment basis functions. Part I: Basic formulation and parcel model test, J. Atmos. Sci., 52, 4344–4366, 1995. </mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple"> Heymsfield, A. J. and Sabin, R. M.: Cirrus crystal nucleation by homogeneous freezing of solution droplets, J. Atmos. Sci., 46, 2252–2264, 1989. </mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Heymsfield, A. and Iaquinta, J.: Cirrus crystal terminal velocities, J. Atmos. Sci., 57, 916–938, 2000. </mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple"> Heymsfield, A. and McFarquhar, G. M.: Mid-latitude and tropical cirrus: Microphysical properties. In: \it Cirrus [D.K. Lynch, K. Sassen, D. O&apos;C. Starr, G. Stephens (Eds.)]. Oxford University Press, Oxford, U.K., 78–101, 2002 </mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple"> Höller, H.: Parameterization of cloud-microphysical processes in a three-dimensional convective mesoscale model, Forschungsbericht, Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt, DFVLR FB 86-02, 82 pp., ISSN 0171-1342, 1986. </mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Hoyle, C., Luo, B., and Peter, T.: The origin of high ice crystal number densities in cirrus clouds, J. Atmos. Sci., 62, 2568–2579, 2005. </mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple"> IPCC: Climate Change 2007: The Physical Science Basis. in: Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Solomon, S., Qin, D., Manning, M., Chen, Z.,Marquis, M., Averyt, K. B., Tignor, M., and Miller, H. L., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 996 pp., 2007. </mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple"> Jawitz, J. W.: Moments of truncated continuous univariate distributions, Adv. Water Res., 27, 269–281, 2004. </mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple"> Jensen, E. J., Toon, O. B., Westphal, D. L., Kinne, S., and Heymsfield, A. J.: Microphysical modeling of cirrus 1. Comparison with 1986 FIRE IFO measurements, J. Geophys. Res., 99(D5), 10421–10442, doi:10.1029/93JD02334, 1994. </mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple"> Kajikawa, M. and Heymsfield, A.: Aggregation of ice crystals, J. Atmos. Sci., 46, 3108–3121, 1989. </mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple"> Kärcher, B.: Supersaturation, dehydration, and denitrification in Arctic cirrus, Atmos. Chem. Phys., 5, 1757–1772, 2005. </mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple"> Kärcher, B. and Lohmann, U.: A Parameterization of cirrus cloud formation: Homogeneous freezing of supercooled aerosols, J. Geophys. Res., 107(D2), 4010, doi:10.1029/2001JD000470, 2002a. </mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple"> Kärcher, B. and Lohmann, U.: A parameterization of cirrus cloud formation: Homogeneous freezing including effects of aerosol size, J. Geophys. Res., 107, D23, D01205, doi:10.1029/2001JD001429, 2002b. </mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple"> Kärcher, B., Hendricks, J., and Lohmann, U.: Physically-based parameterization of cirrus cloud formation for use in global atmospheric models, J. Geophys. Res., 111, D01205, doi:10.1029/2005JD006219, 2006. </mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Kay, J. and Wood, R.: Timescale analysis of aerosol sensitivity during homogeneous freezing and implications for upper tropospheric water vapor budgets, Geophys. Res. Lett., 35, L10809, doi:10.1029/2007GL032628, 2008. </mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Kessler, E.: On the distribution and continuity of water substance in atmospheric circulations, Meteor. Monogr., 32, Am. Meteorol. Soc., 84 pp., Boston, 1969. </mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple"> Koenig, L.: Numerical modeling of ice deposition, J. Atmos. Sci., 28, 226–237, 1971. </mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple"> Koop, T., Luo, B., Tsias, A., and Peter, T.: Water activity as the determinant for homogeneous ice nucleation in aqueous solutions, Nature 406, 611–614, 2000. </mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple"> Krämer, M., Schiller, C., Afchine, A., Bauer, R., Gensch, I., Mangold, A., Schlicht, S., Spelten, N., Sitnikov, N., Borrmann, S., de Reus, M., Spichtinger, P.: Ice supersaturations and cirrus cloud crystal numbers, Atmos. Chem. Phys. Discuss., 8, 21089–21128, 2008. </mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple"> Lee, S.-H., Wilson, J. C. Baumgardner, D., Herman, R. L., Weinstock, E. M., LaFleur, B. G., Kok, G., Anderson, B., Lawson, P., Baker, B., Strawa, A., Pittman, J. V., Reeves, J. M., and Bui, T. P.: New particle formation observed in the tropical/subtropical cirrus clouds, J. Geophys. Res., 109, D20209, doi:10.1029/2004JD005033, 2004. </mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Libbrecht, K. G.: The physics of snow crystals, Rep. Prog. Phys., 68, 855–895, 2005. </mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple"> Lin, R.-F., Starr, D., DeMott, P., Cotton, R., Sassen, K., Jensen, E., Kärcher, B., and Liu, X.: Cirrus Parcel Model Comparison Project. Phase 1: The critical components to simulate cirrus initiation explicitly, J. Atmos. Sci., 59, 2305–2329, 2002. </mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple"> Lin, R.-F., Starr, D., Reichardt, J., and DeMott, P.: Nucleation in synoptically forced cirrostratus, J. Geophys. Res., 110, D08208, doi:10.1029/2004JD005362, 2005. </mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple">Liu, X., Penner, J. E., Ghan, S. J., and Wang, M.: Inclusion of Ice Microphysics in the NCAR Community Atmospheric Model Version 3 (CAM3), J. Climate, 20, 4526–4547, 2007. </mixed-citation>
</ref>
<ref id="ref46">
<label>46</label><mixed-citation publication-type="other" xlink:type="simple">Lohmann, U. and Kärcher, B.: First interactive simulations of cirrus clouds formed by homogeneous freezing in the ECHAM GCM, J. Geophys. Res., 107, 4105, doi:10.1029/2001JD000767, 2002. </mixed-citation>
</ref>
<ref id="ref47">
<label>47</label><mixed-citation publication-type="other" xlink:type="simple">Magee, N., Moyle, A. M., Lamb, D.: Experimental determination of the deposition coefficient of small cirrus-like ice crystals near $-50^\circ$C, Geophys. Res. Lett., 33, L17813, doi:10.1029/2006GL026665, 2006. </mixed-citation>
</ref>
<ref id="ref48">
<label>48</label><mixed-citation publication-type="other" xlink:type="simple">McDonald, J. E.: Use of the electrostatic analogy in studies of ice crystal growth, ZAMP, 14, 610–620, 1963 </mixed-citation>
</ref>
<ref id="ref49">
<label>49</label><mixed-citation publication-type="other" xlink:type="simple"> Meyers, M. P., DeMott, P. J., and Cotton, W. R.: New primary ice-nucleation parameterizations in an explicit cloud model, J. Appl. Meteorol., 31, 708–721, 1992. </mixed-citation>
</ref>
<ref id="ref50">
<label>50</label><mixed-citation publication-type="other" xlink:type="simple"> Minikin, A., Petzold, A., Ström, J., Krejci, R., Seifert, M., van Velthoven, P., Schlager, H., and Schumann, U.: Aircraft observations of the upper tropospheric fine particle aerosol in the Northern and Southern Hemispheres at midlatitudes, Geophys. Res. Lett., 30, 1503, doi:10.1029/2002GL016458, 2003. </mixed-citation>
</ref>
<ref id="ref51">
<label>51</label><mixed-citation publication-type="other" xlink:type="simple">Murphy, D. and Koop, T.: Review of the vapour pressure of ice and supercooled water for atmospheric applications, Q. J. Roy. Meteror. Soc., 131, 1539–1565, 2005. </mixed-citation>
</ref>
<ref id="ref52">
<label>52</label><mixed-citation publication-type="other" xlink:type="simple">Ovarlez, J., Gayet, J.-F., Gierens, K., Ström, J., Ovarlez, H., Auriol, F., Busen, R.,Schumann,U.: Water vapor measurements inside cirrus clouds in northern and southern hemispheres during INCA, Geophys. Res. Lett., doi:10.1029/2001GL014440, 2002. </mixed-citation>
</ref>
<ref id="ref53">
<label>53</label><mixed-citation publication-type="other" xlink:type="simple"> Peter, T., Marcolli, C., Spichtinger, P., Corti, T., Baker M. B., and Koop, T.: When dry air is too humid, Science, 314 (5804), 1399–1400, 2006. </mixed-citation>
</ref>
<ref id="ref54">
<label>54</label><mixed-citation publication-type="other" xlink:type="simple">Peter, T., Kraemer, M., and Moehler, O.: Upper Tropospheric Humidity, SPARC/WCRP Newsletter 30, 9–15, 2008. </mixed-citation>
</ref>
<ref id="ref55">
<label>55</label><mixed-citation publication-type="other" xlink:type="simple">Phillips, V. T. J., Choularton, T. W., Illingworth, A. J., Hogan, R. J., and Field, P. R. Simulations of the glaciation of a frontal mixed-phase cloud with the Explicit Microphysics Model, Q. J. Roy. Meteror. Soc., 129, 1351–1371, 2003. </mixed-citation>
</ref>
<ref id="ref56">
<label>56</label><mixed-citation publication-type="other" xlink:type="simple"> Pruppacher, H. and Klett, J.: Microphysics of Clouds and Precipitation, Kluwer Acad. Pub., Dordrecht, 954 pp., 1997 </mixed-citation>
</ref>
<ref id="ref57">
<label>57</label><mixed-citation publication-type="other" xlink:type="simple">Reisner, J., Rasmussen, R. M., and Bruintjes, R. T.: Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model, Q. J. Roy. Meteror. Soc., 124, 1071–1107, 1998. </mixed-citation>
</ref>
<ref id="ref58">
<label>58</label><mixed-citation publication-type="other" xlink:type="simple">Sassen, K. and Dodd, G. C.: Homogeneous nucleation rate for highly supercooled cirrus cloud droplets, J. Atmos. Sci., 45, 1357–1369, 1988. </mixed-citation>
</ref>
<ref id="ref59">
<label>59</label><mixed-citation publication-type="other" xlink:type="simple">Sassen, K. and Dodd, G. C.: Haze particle nucleation simulations in cirrus clouds, and applications for numerical and lidar studies, J. Atmos. Sci., 46, 3005–3014, 1989. </mixed-citation>
</ref>
<ref id="ref60">
<label>60</label><mixed-citation publication-type="other" xlink:type="simple">Schröder,~F., Kärcher, B., Duroure, C., Ström, J., Petzold, A., Gayet, J.-F., Strauss, B., Wendling, P., and Borrmann, S.: On the transition of contrails into cirrus clouds, J. Atmos. Sci., 57, 464–480, 2000. </mixed-citation>
</ref>
<ref id="ref61">
<label>61</label><mixed-citation publication-type="other" xlink:type="simple">Seifert, A. and Beheng, K. D.: A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description, Meteorol. Atmos. Phys., 92, 45–66, 2005. </mixed-citation>
</ref>
<ref id="ref62">
<label>62</label><mixed-citation publication-type="other" xlink:type="simple"> Smolarkiewicz,~P. and Margolin,L.: On forward-in-time differencing for fluids: an Eulerian/Semi-Lagrangian non-hydrostatic model for stratified flows, Atmos.-Ocean., 35, 127–152, 1997. </mixed-citation>
</ref>
<ref id="ref63">
<label>63</label><mixed-citation publication-type="other" xlink:type="simple"> Smolarkiewicz, P. K. and Margolin, L. G.: MPDATA: A positive definite solver for geophysical flows, J. Comput. Phys., 140, 459–480, 1998. </mixed-citation>
</ref>
<ref id="ref64">
<label>64</label><mixed-citation publication-type="other" xlink:type="simple"> Smolarkiewicz, P., Margolin, L., and Wyszogrodzki, A.: A class of nonhydrostatic global models, J. Atmos. Sci., 58, 349–364, 2001. </mixed-citation>
</ref>
<ref id="ref65">
<label>65</label><mixed-citation publication-type="other" xlink:type="simple">Spichtinger, P., Gierens, K., Leiterer, U., and Dier, H.: Ice supersaturation in the tropopause region over Lindenberg, Germany, Meteorol. Z., 12, 143–156, 2003a. </mixed-citation>
</ref>
<ref id="ref66">
<label>66</label><mixed-citation publication-type="other" xlink:type="simple">Spichtinger, P., Gierens, K., and Read, W.: The global distribution of ice supersaturated regions as seen by the microwave limb sounder, Q. J. Roy. Meteror. Soc., 129, 3391–3410, 2003b. </mixed-citation>
</ref>
<ref id="ref67">
<label>67</label><mixed-citation publication-type="other" xlink:type="simple">Spichtinger, P., Gierens, K., Smit, H. G. J., Ovarlez, J., and Gayet, J.-F.: On the distribution of relative humidity in cirrus clouds. Atmos. Chem. Phys., 4, 639–647, 2004. </mixed-citation>
</ref>
<ref id="ref68">
<label>68</label><mixed-citation publication-type="other" xlink:type="simple">Spichtinger, P., Gierens, K., and Wernli, H.: A case study on the formation and evolution of ice supersaturation in the vicinity of a warm conveyor belt&apos;s outflow region, Atmos. Chem. Phys., 5, 973–987, 2005a. </mixed-citation>
</ref>
<ref id="ref69">
<label>69</label><mixed-citation publication-type="other" xlink:type="simple">Spichtinger, P., Gierens, K., and Dörnbrack, A.: Formation of ice supersaturation by mesoscale gravity waves, Atmos. Chem. Phys., 5, 1243–1255, 2005b. </mixed-citation>
</ref>
<ref id="ref70">
<label>70</label><mixed-citation publication-type="other" xlink:type="simple">Spichtinger P. and Dörnbrack, A.: Microphysical modeling of orographic cirrus clouds, Proceedings of the 12th AMS Conference on Cloud Physics, Madison, USA, 2006. </mixed-citation>
</ref>
<ref id="ref71">
<label>71</label><mixed-citation publication-type="other" xlink:type="simple"> Spichtinger, P. and Gierens, K.: Modelling of cirrus clouds – Part 1b: Structuring cirrus clouds by dynamics, Atmos. Chem. Phys., 9, 707–719, 2009. </mixed-citation>
</ref>
<ref id="ref72">
<label>72</label><mixed-citation publication-type="other" xlink:type="simple">Spichtinger, P. and Gierens, K. M.: Modelling of cirrus clouds – Part 2: Competition of different nucleation mechanisms, Atmos. Chem. Phys. Discuss., 8, 9061–9098, 2008. </mixed-citation>
</ref>
<ref id="ref73">
<label>73</label><mixed-citation publication-type="other" xlink:type="simple"> Starr, D. and Cox, S.: Cirrus clouds. Part I: A Cirrus Cloud Model, J. Atmos. Sci., 42, 2663–2681, 1985. </mixed-citation>
</ref>
<ref id="ref74">
<label>74</label><mixed-citation publication-type="other" xlink:type="simple">Stephens, G.: The influence of radiative transfer on the mass and heat budgets of ice crystals falling in the atmosphere, J. Atmos. Sci., 40, 1729–1739, 1983. </mixed-citation>
</ref>
<ref id="ref75">
<label>75</label><mixed-citation publication-type="other" xlink:type="simple">Tompkins, A., Gierens, K., and Rädel, G.: Ice supersaturation in the ECMWF integrated forecast system, Q. J. Roy. Meteror. Soc., 133, 53–63, 2007. </mixed-citation>
</ref>
<ref id="ref76">
<label>76</label><mixed-citation publication-type="other" xlink:type="simple">Wernli, H. and Davies, H.: A Lagrangian-based analysis of extratropical cyclones. I: The method and some applications, Q. J. Roy. Meteror. Soc., 123, 467–489, 1997. </mixed-citation>
</ref>
<ref id="ref77">
<label>77</label><mixed-citation publication-type="other" xlink:type="simple">Walcek, C.: Minor flux adjustment near mixing ratio extremes for a simplified yet highly accurate monotonic calculation of tracer advection, J. Geophys. Res., 105, 9335–9348, 2000. </mixed-citation>
</ref>
<ref id="ref78">
<label>78</label><mixed-citation publication-type="other" xlink:type="simple">Wacker, U. and Seifert, A.: Evolution of rain water profiles resulting from pure sedimentation: Spectral vs parameterized description, Atmos. Res., 58, 19–39, 2001. </mixed-citation>
</ref>
<ref id="ref79">
<label>79</label><mixed-citation publication-type="other" xlink:type="simple">Wendisch, M., Pilewskie, P., Pommier, J., Howard, S., Yang, P., Heymsfield, A. J., Schmitt, C. G., Baumgardner, D., and Mayer, B.: Impact of cirrus crystal shape on solar spectral irradiance: A case study for subtropical cirrus, J. Geophys. Res., 110, D03202, doi:10.1029/2004JD005294, 2005. </mixed-citation>
</ref>
<ref id="ref80">
<label>80</label><mixed-citation publication-type="other" xlink:type="simple">Wendisch, M., Yang, P., and Pilewskie, P.: Effects of ice crystal habit on thermal infrared radiative properties and forcing of cirrus, J. Geophys. Res., 112, D08201, doi:10.1029/2006JD007899, 2007. </mixed-citation>
</ref>
<ref id="ref81">
<label>81</label><mixed-citation publication-type="other" xlink:type="simple"> Wood, S. E., Baker, M. B., and Calhoun, D.: New model for the vapor growth of hexagonal ice crystals in the atmosphere, J. Geophys. Res., 106, 4845–4870, 2001. </mixed-citation>
</ref>
</ref-list>
</back>
</article>