ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-12-9275-2012 Parameterization of homogeneous ice nucleation for cloud and climate models based on classical nucleation theory Khvorostyanov V. I. 1 Curry J. A. 2 Central Aerological Observatory, Dolgoprudny, Moscow Region, Russia School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia, USA 11 10 2012 12 19 9275 9302 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. This article is available from http://www.atmos-chem-phys.net/12/9275/2012/acp-12-9275-2012.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/12/9275/2012/acp-12-9275-2012.pdf

A new analytical parameterization of homogeneous ice nucleation is developed based on extended classical nucleation theory including new equations for the critical radii of the ice germs, free energies and nucleation rates as simultaneous functions of temperature and water saturation ratio. By representing these quantities as separable products of the analytical functions of temperature and supersaturation, analytical solutions are found for the integral-differential supersaturation equation and concentration of nucleated crystals. Parcel model simulations are used to illustrate the general behavior of various nucleation properties under various conditions, for justifications of the further key analytical simplifications, and for verification of the resulting parameterization. <br><br> The final parameterization is based upon the values of the supersaturation that determines the current or maximum concentrations of the nucleated ice crystals. The crystal concentration is analytically expressed as a function of time and can be used for parameterization of homogeneous ice nucleation both in the models with small time steps and for substep parameterization in the models with large time steps. The crystal concentration is expressed analytically via the error functions or elementary functions and depends only on the fundamental atmospheric parameters and parameters of classical nucleation theory. The diffusion and kinetic limits of the new parameterization agree with previous semi-empirical parameterizations.

 References Barahona, D. and Nenes, A.: Parameterization of cirrus cloud formation in large-scale models: Homogeneous nucleation, J. Geophys. Res., 113, D11211, http://dx.doi.org/10.1029/2007JD009355doi:10.1029/2007JD009355, 2008. Bertram, A. K., Koop, T., Molina, L. T., and Molina, M. J.: Ice formation in (NH$_4)_2$SO<sub>4</sub>-H<sub>2</sub>O particles, J. Phys. Chem. A, 104, 584–588, 2000. Chen Y., DeMott, P. J., Kreidenweis, S. M., Rogers, D. C., and Sherman, E.: Ice formation by sulfate and sulfur acid aerosols under upper-tropospheric conditions, J. Atmos. Sci., 57, 3752–3766, 2000. Clegg, S. I., Brimblecombe, P., and Wexler, A. S.: A thermodynamic model of the system H$^+$-NH$_4^+$-SO$_4^2-$-NO$^3-$-H<sub>2</sub>O at tropospheric temperatures, J. Phys. Chem., 102, 2137–2154, 1998. Curry, J. A. and Khvorostyanov, V. I.: Assessment of some parameterizations of heterogeneous ice nucleation in cloud and climate models, Atmos. Chem. Phys., 12, 1151–1172, http://dx.doi.org/10.5194/acp-12-1151-2012doi:10.5194/acp-12-1151-2012, 2012. Defay, R., Prigogine, I., and Bellemans, A.: Surface Tension and Absorption, 432 pp., Wiley, New York, 1966. DeMott, P. J.: Laboratory studies of cirrus cloud processes, in: \textit"Cirrus", edited by: Lynch, D., Sassen, K., Starr, D. O'C., and Stephens, G., Oxford University Press, New York, 102–135, 2002. DeMott, P. J., Meyers, M. P., and Cotton, W. R.: Parameterization and impact of ice initiation processes relevant to numerical model simulation of cirrus clouds, J. Atmos. Sci., 51, 77–90, 1994. Dufour, L. and Defay, R.: Thermodynamics of Clouds, 255 pp., Academic Press, New York, 1963. Eadie, W. J.: A molecular theory of the homogeneous nucleation of ice from supercooled water, PhD Dissertation, University of Chicago, Cloud Physics Lab, Tech. Note 40, 117 pp., 1971. Fan, J., Ghan, S., Ovchinnikov, M., Liu, X., Rasch, P. J., and Korolev, A.: Representation of Arctic mixed-phase clouds and the Wegener-Bergeron-Findeisen process in climate models: Perspectives from a cloud-resolving study, J. Geophys. Res., 116, D00T07, http://dx.doi.org/10.1029/2010JD015375doi:10.1029/2010JD015375, 2011. Feistel, R.: TEOS-10: A new international oceanographic standard for seawater, ice, fluid water and humid air, International Journal of Thermophysics, http://dx.doi.org/10.1007/s10765-010-0901-ydoi:10.1007/s10765-010-0901-y, 2012. Feistel, R. and Wagner, W.: A new equation of state for H<sub>2</sub>O ice Ih, J. Phys. Chem. Ref. Data, 35, 1021–1047, http://dx.doi.org/10.1063/1.2183324doi:10.1063/1.2183324, 2006. Ford, I. J: How aircraft nucleate ice particles: A simple model, J. Aerosol Sci., 29, S1117, http://dx.doi.org/10.1016/S0021-8502(98)90741-8doi:10.1016/S0021-8502(98)90741-8, 1998a. Ford, I. J.: Ice nucleation in jet aircraft exhaust plumes, in: Air Pollution Research Report 68: Pollution from aircraft emissions in the North Atlantic flight corridor (POLINAT2), edited by: Schumann, U., Report EUR 18877, European Commission, 1998, 269–287, 1998b. Frenkel, Ya. I.: Kinetic Theory of Liquids, Oxford University Press, 592 pp., 1946. Fridlind, A., Ackerman, A. S., Jensen, E. J., Heymsfield, A. J., Poellot, M. R., Stevens, D. E., Wang, D., Miloshevich, L. M., Baumgardner, D., Lawson, R. P., Wilson, J. C., Flagan, R. C., Seinfeld, J. H., Jonsson, H. H., VanReken, T. M., Varutbangkul, V., and Rissman, T. A.: Evidence for the predominance of mid-tropospheric aerosols as subtropical anvil cloud nuclei, Science, 304, 718–722, 2004. Fuchs, N. A.: Evaporation and Droplet Growth in Gaseous Media, Pergamon Press, 242 pp., 1959. Gayet, J.-F., Ovarlez, J., Shcherbakov, V., Ström, J., Schumann, U., Minikin, A., Auriol, F., Petzold, A., and Monier, M.: Cirrus cloud microphysical and optical properties at southern and northern midlatitudes during the INCA experiment, J. Geophys. Res., 109, D20206, http://dx.doi.org/10.1029/2004JD004803doi:10.1029/2004JD004803, 2004. Gettelman, A., Liu, X., Ghan, S. J., Morrison, H., Park, S., and Conley, A. J.: Global simulations of ice nucleation and ice supersaturation with an improved cloud scheme in the Community Atmosphere Model, J. Geophys. Res., 115, D18216, http://dx.doi.org/10.1029/2009JD013797doi:10.1029/2009JD013797, 2010. Ghan, S., Chuang, C., and Penner, J.: A parameterization of cloud droplet nucleation. Part 1, Single aerosol species, Atmos. Res., 30, 197–222, 1993. Ghan, S. J., Abdul-Razzak, H., Nenes, A., Ming, Y., Liu, X., Ovchinnikov, M., Shipway, B., Meskhidze, N., Xu, J., and Shi, X.: Droplet nucleation: Physically-based parameterizations and comparative evaluation, J. Adv. Model. Earth Syst., 3, M10001, http://dx.doi.org/10.1029/2011MS000074doi:10.1029/2011MS000074, 2011. Gierens, K. M., Monier, M., and Gayet, J.-F.: The deposition coefficient and its role for cirrus clouds, J. Geophys. Res., 108, 4069, http://dx.doi.org/10.1029/2001JD001558doi:10.1029/2001JD001558, 2003. Grabowski, W. W. and Morrison, H.: Toward the mitigation of spurious cloud-edge supersaturation in cloud models, Mon. Weather Rev., 136, 1224–1234, http://dx.doi.org/10.1175/2007MWR2283.1doi:10.1175/2007MWR2283.1, 2008. Gradshteyn, I. S. and Ryzhik, I. M.: Table of Integrals, Series, and Products, Fifth Ed., Academic, San Diego, Calif., 1204 pp., 1994. Haag, W., 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, http://dx.doi.org/10.5194/acp-3-1791-2003doi:10.5194/acp-3-1791-2003, 2003. Hellmuth, O., Khvorostyanov, V. I., Curry, J. A., Shchekin, A. K., Schmelzer, J. W. P., and. Baidakov, V. G: Review on the Phenomenology and Mechanism of Atmospheric Ice Formation: Selected Questions of Interest, in: Nucleation Theory and Applications, edited by: Schmelzer, J. W. P., Röpke, G., and Priezzhev, V. B., Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna, ISBN 978-5-9530-0301-8, 2012a. Hellmuth, O., Khvorostyanov, V. I., Curry, J. A., Shchekin, A. K., Schmelzer, J. W. P., Feistel, R., Djikaev, Y. S., and Baidakov, V. G.: Theoretical Aspects of Atmospheric Ice Formation, in: Nucleation Theory and Applications, edited by: Schmelzer, J. W. P., Special Issues. Review Series on Selected Topics of Atmospheric Sol Formation, Vol. 5, Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna, 548 pp., 2012b. Heymsfield, A. J. and Miloshevich, L. M.: Homogeneous ice nucleation and supercooled liquid water in orographic wave clouds, J. Atmos. Sci., 50, 2335–2353, 1993. Heymsfield, A. J. and Miloshevich, L. M.: Relative humidity and temperature influences on cirrus formation and evolution: Observations from wave clouds and FIRE II, J. Atmos. Sci., 52, 4302–4326, 1995. Holten, V., Bertrand, C. E., Anisimov, M. A., and Sengers, J. V.: Thermodynamic modeling of supercooled water. Technical report for the International Association for the Properties of Water and Steam (IAPWS) (September 2011), Tech. rep., Institute for Physical Science and Technology and Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742, USA, 2011. Holten, V., Bertrand, C. E., Anisimov, M. A., and Sengers, J. V.: Thermodynamics of supercooled water, J. Chem. Phys., 136, 094507, http://dx.doi.org/10.1063/1.3690497doi:10.1063/1.3690497, 2012. IAPWS: Guideline on a Low-Temperature Extension of the IAPWS-95 Formulation for Water Vapor, Tech. rep., The International Association for the Properties of Water and Steam, Boulder, Colorado, USA, September/October 2012, 2012. Ice Physics and the Natural Environment, Proc. NATO Advanced Research Workshop, v. 56, edited by: Wettlaufer, J. S., Dash, J. G., and Untersteiner, N., Springer, Berlin, 356 pp., 1999. IOC, SCOR and IAPSO: The International Thermodynamic Equation of Seawater – 2010: Calculation and Use of Thermodynamic Properties, written by: McDougall,T. J., Feistel, R., Wright, D. G., Pawlowicz, R., Millero, F. J., Jackett, D. R., King, B. A., Marion, G. M., Seitz, S., Spitzer, P., and Chen, C. T. A., Tech. rep., Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp., Paris 2010, http://www.teos-10.org, 2010. Jeffery, C. A. and Austin, P. H.: Homogeneous nucleation of supercooled water: results from a new equation of state, J. Ceophys. Res., 102, 25269–25279, 1997. 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, 10421–10442, 1994. Kanno, H. and Angell, C. A.: Homogeneous nucleation and glass formation in aqueous alkali halide solutions at high pressures, J. Phys. Chem., 81, 2639–2643, 1977. Kärcher, B. and Lohmann, U.: A parameterization of cirrus cloud formation: Homogeneous freezing of supercooled aerosols, J. Geophys. Res., 107, 4010, http://dx.doi.org/10.1029/2001JD000470doi:10.1029/2001JD000470, 2002a. Kärcher, B. and Lohmann, U.: A Parameterization of cirrus cloud formation: Homogeneous freezing including effects of aerosol size, J. Geophys. Res., 107, 4698, http://dx.doi.org/10.1029/2001JD001429doi:10.1029/2001JD001429, 2002b. Kashchiev, D.: Nucleation: Basic Theory with Applications, Batterworth-Heineman, Oxford, 512 pp., 2000. Khain, A. P., Pokrovsky, A., Pinsky, M., Seifert, A., and Phillips, V.: Simulation of effects of atmospheric aerosols on deep turbulent convective clouds using a spectral microphysics mixed-phase cumulus cloud model. Part I: Model description and possible applications, J. Atmos. Sci., 61, 2963–2982, 2004. Khairoutdinov, M. F. and Randall, D.: Cloud resolving modeling of the ARM summer 1997 IOP: Model formulation, results, uncertainties, and sensitivities, J. Atmos. Sci., 60, 607–625, 2003. Khvorostyanov, V. I. and Curry, J. A.: A new theory of heterogeneous ice nucleation for application in cloud and climate models, Geophys. Res. Lett., 27, 4081–4084, 2000. Khvorostyanov, V. I. and Curry, J. A.: Thermodynamic theory of freezing and melting of water and aqueous solutions, J. Phys. Chem. A, 108, 11073–11085, 2004a. Khvorostyanov, V. I. and Curry, J. A.: The theory of ice nucleation by heterogeneous freezing of deliquescent mixed CCN. Part 1: Critical radius, energy and nucleation rate, J. Atmos. Sci., 61, 2676–2691, 2004b. Khvorostyanov, V. I. and Curry, J. A.: The theory of ice nucleation by heterogeneous freezing of deliquescent mixed CCN. Part 2: Parcel model simulation, J. Atmos. Sci., 62, 261–285 2005. Khvorostyanov, V. I. and Curry, J. A.: Kinetics of cloud drop formation and its parameterization for cloud and climate models, J. Atmos. Sci., 65, 2784–2802, 2008. Khvorostyanov, V. I. and Curry, J. A.: Critical humidities of homogeneous and heterogeneous ice nucleation: inferences from extended classical nucleation theory, J. Geophys. Res., 114, D04207, http://dx.doi.org/10.1029/2008JD011197doi:10.1029/2008JD011197, 2009a. Khvorostyanov, V. I. and Curry, J. A.: Parameterization of cloud drop activation based on analytical asymptotic solutions to the supersaturation equation, J. Atmos. Sci., 66, 1905–1925, 2009b. Khvorostyanov, V. I. and Sassen, K.: Towards the theory of homogeneous nucleation and its parameterization for cloud models, Geophys. Res. Lett., 25, 3155–3158, 1998a. Khvorostyanov, V. I. and Sassen, K.: Cirrus cloud simulation using explicit microphysics and radiation. Part I, Model description, J. Atmos. Sci., 55, 1808–1821, 1998b. Khvorostyanov, V. I. and Sassen, K.: Microphysical processes in cirrus and their impact on radiation: A mesoscale modeling perspective, in: Cirrus, edited by: Lynch, D., Sassen, K., Starr, D. O'C., and Stephens, G., Oxford University Press, New York, 397–432, 2002. Khvorostyanov, V. I., Curry, J. A., Pinto, J. O., Shupe, M., Baker, B., and Sassen, K.: Modeling with explicit spectral water and ice microphysics of a two-layer cloud system of altostratus and cirrus observed during the FIRE Arctic Clouds Experiment, J. Geophys. Res., 106, 15099–15112, 2001. Khvorostyanov, V. I., Curry, J. A., Gultepe, I., and Strawbridge, K.: A springtime mixed-phase cloud over the Beaufort Sea polynya: Three-dimensional simulation with explicit spectral microphysics and comparison with observations, J. Geophys. Res., 108, 4296, http://dx.doi.org/10.1029/2001JD001489doi:10.1029/2001JD001489, 2003. Khvorostyanov, V. I., Morrison, H., Curry, J. A., Baumgardner, D., and Lawson, P.: High supersaturation and modes of ice nucleation in thin tropopause cirrus: Simulation of the 13 July 2002 Cirrus Regional Study of Tropical Anvils and Cirrus Layers case, J. Geophys. Res., 111, D02201, http://dx.doi.org/10.1029/2004JD005235doi:10.1029/2004JD005235, 2006. Klein, S. A.,. McCoy, R. B, Morrison, H., Ackerman, A. S., Avramov, A., de Boer, G., Chen, M., Cole, J. N. S., Del Genio, A. D., Falk, M., Foster, M. J., Fridlind, A., Golaz, J.-C., Hashino, T., Harrington, J. Y., Hoose, C., Khairoutdinov, M. F., Larson, V. E., Liu, X, Luo, Y., McFarquhar, G. M., Menon, S., Neggers, R. A. J., Park, S., Poellot, M. R., Schmidt, J. M., Sednev, I., Shipway, B. J., Shupe, M. D., Spangenberg, D. A., Sud, Y. C., Turner, D. D., Veron, D. E., von Salzen, K., Walker, G. K., Wang, Z., Wolf, A. B., Xie, S., Xu, K.-M., Yang, F., and Zhango G.: Intercomparison of model simulations of mixed-phase clouds observed during the ARM Mixed-Phase Arctic Cloud Experiment. I. Single-layer cloud, Q. J. Roy. Meteor. Soc., 135, 979–1002, 2009. Köhler, H.: The nucleus in and the growth of hygroscopic droplets, Trans. Farad. Soc., 32, 1152–1161, 1936. Koop, T. and Zobrist, B.: Parameterizations for ice nucleation in biological and atmospheric systems, Phys. Chem. Chem. Phys., 11, 10839–10850, 2009. Koop, T., Ng, H. P., Molina, L. T., and Molina, M. J.: A new optical technique to study aerosol phase transitions: The nucleation of ice from H<sub>2</sub>SO<sub>4</sub> aerosols, J. Phys. Chem. A, 102, 8924–8931, 1998. Koop, T., Luo, B. P., Tsias, A., and Peter, T.: Water activity as the determinant for homogeneous ice nucleation in aqueous solutions, Nature, 406, 611–614, 2000. Krakovskaia, S. V. and Pirnach, A. M.: A theoretical study of the microphysical structure of mixed stratiform frontal clouds and their precipitation, Atmos. Res., 47–48, 491–503, 2004. Laaksonen, A., Talanquer, V., and Oxtoby, D. W.: Nucleation: Measurements, theory and atmospheric applications, Ann. Rev. Phys. Chem., 46, 489–524, 1995. Lin, R.-F.: A numerical study of the evolution of nocturnal cirrus by a two-dimensional model with explicit microphysics. PhD thesis, The Pennsylvania State University, 199 pp., 1997. Lin, R.-F., Starr, D. O'C., DeMott, P. J., 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. Liu, X. H. and Penner, J. E.: Ice nucleation parameterization for global models, Meteorol. Z., 14, 499–514, 2005. Lohmann, U. and Kärcher, B.: First interactive simulations of cirrus clouds formed by homogeneous freezing in the ECHAM general circulation model, J. Geophys. Res., 107, 4105, http://dx.doi.org/10.1029/2001JD000767doi:10.1029/2001JD000767, 2002. Malkin, T. L., Murray, B. J., Brukhno, A. V., Anwar, J., and Salzmann, C. G.: Structure of ice crystallized from supercooled water, P. Natl. Acad. Sci., 109, 1041–1045, http://dx.doi.org/10.1073/pnas.1113059109doi:10.1073/pnas.1113059109, 2012. Martin, S. T.: Phase transitions of aqueous atmospheric particles, Chem. Rev., 100, 3403–3453, 2000. McDougall, T. J., Feistel, R., Millero, F. J., Jackett, D. R., Wright, D. G., King, B. A., Marion, G. M., Chen, C., Spitzer, P., and Seitz, S.: The International Thermodynamic Equation Of Seawater 2010 (TEOS-10): Calculation and Use of Thermodynamic Properties, UNESCO 2009, IOC Manuals and Guides, 150 pp., www.teos10.org, 2010. Meyers, M. P., DeMott, P. J., and Cotton, W. R.: New primary ice-nucleation parameterizations in an explicit cloud model, J. Appl. Meteor., 31, 708–721, 1992. Mishima, O. and Stanley, H. E.: The relationship between liquid, supercooled and glassy water, Nature, 396, 329–335, 1998. Monier, M., Wobrock, W., Gayet, J.-F., and Flossmann, A.: Development of a detailed microphysics cirrus model tracking aerosol particle's histories for interpretation of the recent INCA campaign, J. Atmos. Sci., 63, 504–525, 2006. Morrison, H. and Gettelman, A.: A new two-moment bulk stratiform cloud microphysics scheme in the community atmosphere model, version 3(CAM3). Part I: Description and numerical tests, J. Clim., 21, 3642–3659, http://dx.doi.org/10.1175/2008JCLI2105.1doi:10.1175/2008JCLI2105.1, 2008. Morrison, H., Curry, J. A., and Khvorostyanov, V. I.: A new double-moment microphysics parameterization for application in cloud and climate models, Part 1: Description, J. Atmos. Sci., 62, 3683–3704, 2005. Murray, B. J. and Bertram, A. K.: Formation and stability of cubic ice in water droplets, Phys. Chem. Chem. Phys., 8, 186–192, 2006. Murray, B. J., Knopf, D. A., and Bertram, A. K.: The formation of cubic ice under conditions relevant to Earth's atmosphere, Nature, 434, 202–205, 2005. Murray, B. J., Broadley S. L., Wilson, T. W., Bull, S. J., Wills, R. H., Christenson, H. K., and Murray E. J.: Kinetics of the homogeneous freezing of water, Phys. Chem. Chem. Phys., 12, 10380–10387, 2010. Ovarlez, J., Gayet, J.-F., Gierens, K., Ström, J., Ovarlez, H., Auriol, F., Busen, R., and Schumann, U.: Water vapour measurements inside cirrus clouds in Northern and Southern hemispheres during INCA, Geophys. Res. Lett., 29, 1813, http://dx.doi.org/10.1029/2001GL014440doi:10.1029/2001GL014440, 2002. Pruppacher, H. R. and Klett, J. D.: Microphysics of Clouds and Precipitation, 2nd ed., Kluwer Academic Publishers: Boston, MA, 954 pp., 1997. Randall, D., Krueger, S., Bretherton, C., Curry, J., Duynkerke, P., Moncrieff, M., Ryan, B., Starr, D., Miller, M., Rossow, W., Tselioudis, G., and Wielicki, B.: Confronting models with data. The GEWEX Cloud Systems Study, B. Am. Meteorol. Soc., 84, 455–469, 2003. Rasmussen, D. H.: Thermodynamic and nucleation phenomena: A set of experimental observations, J. Cryst. Growth, 56, 56–66, 1982. Ren, C. and MacKenzie, A. R.: Cirrus parameterisation and the role of ice nuclei, Q. J. Roy. Meteorol. Soc., 131, 1585–1605, 2005. Ren, C. and MacKenzie, A. R.: Closed-form approximations to the error and complementary error functions and their applications in atmospheric science, Atmos. Sci. Lett., 8, 70–73, http://dx.doi.org/10.1002/asl.154doi:10.1002/asl.154, 2007. Sassen, K. and Benson, S.: Ice nucleation in cirrus clouds: A model study of the homogeneous and heterogeneous nucleation modes, Geophys. Res. Lett., 27, 521–524, 2000. Sassen, K. and Dodd, G. C.: Homogeneous nucleation rate for highly supercooled cirrus cloud droplets, J. Atmos. Sci., 45, 1357–1369, 1988. Sassen, K. and Dodd, G. C.: Haze particle nucleation simulation in cirrus clouds, and application for numerical and lidar studies, J. Atmos. Sci., 46, 3005–3014, 1989. Sassen, K., Wang, Z., Khvorostyanov, V. I., Stephens, G. L., and Bennedetti, A.: Cirrus cloud ice water content radar algorithm evaluation using an explicit cloud microphysical model, J. Appl. Meteorol., 41, 620–628, 2002. Sedunov, Y. S.: Physics of Drop Formation in the Atmosphere, Wiley, New York, 234 pp., 1974. 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, http://dx.doi.org/10.1007/s00703-005-0112-4doi:10.1007/s00703-005-0112-4, 2006. Seinfeld, J. H. and Pandis, S. N.: Atmospheric Chemistry and Physics, Wiley, New York, 1326 pp., 1998. Slezov, V. V. and Schmelzer, J. W. P.: Kinetics of nucleation–growth processes: the first stages, in: Nucleation Theory and Applications, edited by: Schmelzer, J. W. P., Röpke, G., and Priezzhev, V. B., 6–81, JINR, Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna, ISBN 5-85165-539-9, http://theor.jinr.ru/meetings/2012/nta/, 1999. Spice, A., Johnson, D. W., Brown, P. R. A., Darlison, A. G., and Saunders, C. P. R.: Primary ice nucleation in orographic cirrus cloud: A numerical simulation of the microphysics, Q. J. Roy. Meteorol. Soc., 125, 1637–1667, 1999. Ström, J., Seifert, M., Kärcher, B., Ovarlez, J., Minikin, A., Gayet, J.-F., Krejci, R., Petzold, A., Auriol, F., Haag, W., Busen, R., Schumann, U., and Hansson, H. C.: Cirrus cloud occurrence as function of ambient relative humidity: a comparison of observations obtained during the INCA experiment, Atmos. Chem. Phys., 3, 1807–1816, http://dx.doi.org/10.5194/acp-3-1807-2003doi:10.5194/acp-3-1807-2003, 2003. Sud, Y. C., Wilcox, E., Lau, W. K.-M., Walker, G. K., Liu, X.-H., Nenes, A., Lee, D., Kim, K.-M., Zhou, Y., and Bhattacharjee, P. S.: Sensitivity of boreal-summer circulation and precipitation to atmospheric aerosols in selected regions – Part 1: Africa and India, Ann. Geophys., 27, 3989–4007, http://dx.doi.org/10.5194/angeo-27-3989-2009doi:10.5194/angeo-27-3989-2009, 2009. Tao, W.-K., Chen, J.-P., Li, Z., Wang, C., and Zhang, C.: Impact of aerosols on convective clouds and precipitation, Rev. Geophys., 50, RG2001, http://dx.doi.org/10.1029/2011RG000369doi:10.1029/2011RG000369, 2012. Twomey, S.: The nuclei of natural cloud formation. Part II: The supersaturation in natural clouds and the variation of cloud droplet concentration, Pure Appl. Geophys., 43, 243–249, 1959. Veltishchev, N. F., Zhupanov, V. D., and Pavlyukov, Yu. B.: Short-range forecast of heavy precipitation and strong wind using the convection-allowing WRF models, Russian Meteorol. Hydrol., 36, 47–58, 2011. Xue, L., Teller, A., Rasmussen, R., Geresdi, I., Pan, Z.: Effects of aerosol solubility and regeneration on warm-phase orographic clouds and precipitation simulated by a detailed bin microphysical scheme, J. Atmos. Sci., 67, 3336–3354, 2010. Zhang, H., Sokolik, I. N., and Curry, J. A.: Impact of dust aerosols on Hurricane Helene's early development through the deliquescent heterogeneous freezing mode, Atmos. Chem. Phys. Discuss., 11, 14339–14381, http://dx.doi.org/10.5194/acpd-11-14339-2011doi:10.5194/acpd-11-14339-2011, 2011.