ACP Atmospheric Chemistry and Physics ACP Atmos. Chem. Phys. 1680-7324 Copernicus Publications Göttingen, Germany 10.5194/acp-9-6229-2009 Factors controlling contrail cirrus optical depth Kärcher B. 1 Burkhardt U. 1 Unterstrasser S. 1 Minnis P. 2 Deutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany National Aeronautics and Space Administration (NASA), Langley Research Center, Hampton, VA, USA 31 08 2009 9 16 6229 6254 Copyright: © 2009 B. Kärcher et al. 2009 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://acp.copernicus.org/articles/9/6229/2009/acp-9-6229-2009.html The full text article is available as a PDF file from https://acp.copernicus.org/articles/9/6229/2009/acp-9-6229-2009.pdf

Aircraft contrails develop into contrail cirrus by depositional growth and sedimentation of ice particles and horizontal spreading due to wind shear. Factors controlling this development include temperature, ice supersaturation, thickness of ice-supersaturated layers, and vertical gradients in the horizontal wind field. An analytical microphysical cloud model is presented and validated that captures these processes. Many individual contrail cirrus are simulated that develop differently owing to the variability in the controlling factors, resulting in large samples of cloud properties that are statistically analyzed. Contrail cirrus development is studied over the first four hours past formation, similar to the ages of line-shaped contrails that were tracked in satellite imagery on regional scales. On these time scales, contrail cirrus optical depth and microphysical variables exhibit a marked variability, expressed in terms of broad and skewed probability distribution functions. Simulated mean optical depths at a wavelength of 0.55 <i>&mu;</i>m range from 0.05-0.5 and a substantial fraction 20-50% of contrail cirrus stay subvisible (optical depth <0.02), depending on meteorological conditions. <br><br> A detailed analysis based on an observational case study over the continental USA suggests that previous satellite measurements of line-shaped persistent contrails have missed about 89%, 50%, and 11% of contrails with optical depths 0-0.05, 0.05-0.1, and 0.1-0.2, respectively, amounting to 65% of contrail coverage of all optical depths. When comparing observations with simulations and when estimating the contrail cirrus climate impact, not only mean values but also the variability in optical depth and microphysical properties need to be considered.

 References Ackerman, S. A., Holz, R. E., Frey, R., Eloranta, E. W., Maddux, B. C., and McGill, M.: Cloud detection with MODIS. P}art&nbsp;{II}: {Validation, J. Atmos. Oceanic Sci., 25, 1073–1086, 2008. Ansmann, A.: Molecular-backscatter lidar profiling of the volume scattering coefficient in cirrus. In: <i>Cirrus</i>, edited by: Lynch, D. K., Sassen, K., Starr, D. O'C., and Stephens, G. , Oxford Univ.\ Press, N.Y., 197–210, 2002. Atlas, D., Wang, Z., and Duda, D. P.: Contrails to cirrus – {M}orphology, microphysics, and radiative properties, J. Appl. Meteorol. Clim., 45, 5–19, 2006. Benjamin, S. G., Dévényi, D., Weygandt, S. S., Brundage, K. J., Brown, J. M., Grell, G. A., Kim, D., Schwartz, B. E., Smirnova, T. G., Smith, T. L., and Manikin, G. S.: An hourly assimilation/forecast cycle: T}he {RUC, Mon. Weather Rev., 132, 495–518, 2004. Betancor-Gothe, M. and Grassl, H.: Satellite remote sensing of the optical depth and mean size of thin cirrus and contrails, Theor. Appl. Clim., 48, 101–113, 1993. Burkhardt, U. and Kärcher, B.: Process-based simulation of contrail cirrus in a global climate model, J. Geophys. Res., 114, D16201, https://doi.org/10.1029/2008JD011491, 2009. Burkhardt, U., Kärcher, B., and Schumann, U.: Global modeling of the contrail cirrus climate impact, Bull. Amer. Meteorol. Soc., 90, in press, 2009. Carlin, B., Fu, Q., Lohmann, U., Mace, G. G., Sassen, K., and Comstock, J. M.: High cloud horizontal inhomogeneity and solar albedo bias, J. Clim., 15, 2321–2339, 2002. Comstock, J. M., Ackerman, T. P., and Mace, G. G.: Ground-based lidar and radar remote sensing of tropical cirrus clouds at {N}auru {I}sland: {C}loud statistics and radiative impacts, J. Geophys. Res., 107, 4714, https://doi.org/10.1029/2002JD002203, 2002. Delanoë, J., Protat, A., Testud, J., Bouniol, D., Heymsfield, A. J., Bansemer, A., Brown, P. R. A., and Forbes, R. M.: Statistical properties of the normalized ice particle size distribution, J. Geophys. Res., 110, D10201, https://doi.org/10.1029/2004JD005405, 2005. Dobbie, S. and Jonas, P. R.: Radiative influences on the structure and lifetime of cirrus clouds, Q. J. Roy. Meteorol. Soc., 127, 2663–2682, 2001. Dowling, D. R. and Radke, L. F.: A summary of the physical properties of cirrus clouds, J. Appl. Meteorol., 29, 970–978, 1990. Duda, D. P. and Spinhirne, J. D.: Split-window retrieval of particle size and optical depth in contrails located above horizontally inhomogeneous clouds, Geophys. Res. Lett., 23, 3711–3714, 1996. Duda, D. P., Minnis, P., and Nguyen, L.: Estimates of cloud radiative forcing in contrail clusters using GOES imagery, J. Geophys. Res., 106, 4927–4937, 2001. Duda, D. P., Minnis, P., Nguyen, L., and Palikonda, R.: A case study of the development of contrail clusters over the Great Lakes, J. Atmos. Sci., 61, 1132–1146, 2004. Dürbeck, T. and Gerz, T.: Dispersion of aircraft exhausts in the free atmosphere, J. Geophys. Res., 101, 26007–26015, 1996. Ebert, E. E. and Curry, J. A.: A parameterization of ice cloud optical properties for climate models, J. Geophys. Res., 97, 3831–3836, 1992. Febvre, G., Gayet, J.-F., Minikin, A., Schlager, H., Shcherbakov, V., Jourdan, O., Busen, R., Fiebig, M., Kärcher, B., and Schumann, U.: On optical and microphysical characteristics of contrails and cirrus, J. Geophys. Res., 114, D02204, https://doi.org/10.1029/2008JD010184, 2009. Field, P. R. and Heymsfield, A. J.: Aggregation and scaling of ice crystal size distributions, J. Atmos. Sci., 60, 544–560, 2003. Forster, P., Ramaswamy, V., Artaxo, P., et al.: Changes in atmospheric constituents and in radiative forcing. I}n: {C}limate {C}hange 2007: {T}he {P}hysical {S}cience {B}asis. Contribution of WG&nbsp;I to the 4th {A}ssessment {R}eport of the {IPCC, edited by: Solomon, S., Qin, D., Manning, M., et al., Cambridge Univ. Press, Cambridge, UK, and NY, USA, 2007. Freudenthaler, V., Homburg, F., and Jäger, H.: Contrail observations by ground-based scanning Lidar: Cross-sectional growth, Geophys. Res. Lett., 22, 3501–3504, 1995. Fu, Q. and Liou, K. N.: Parameterization of the radiative properties of cirrus clouds, J. Atmos. Sci., 50, 2008–2025, 1993. Fu, Q., Carlin, B., and Mace, G.: Cirrus horizontal inhomogeneity and OLR bias, Geophys. Res. Lett., 27, 3341–3344, 2000. Gayet, J.-F., Febvre, G., Brogniez, G., Chepfer, H., Renger, W., and Wendling, P.: Microphysical and optical properties of cirrus and contrails, J. Atmos. Sci., 53, 126–138, 1996. Gayet, J.-F., Auriol, F., Minikin, A., Ström, J., Seifert, M., Krejci, R., Petzold, A., Febvre, G., and Schumann, U.: Quantitative measurement of the microphysical and optical properties of cirrus clouds with four different in situ probes: {E}vidence of small ice crystals, Geophys. Res. Lett., 29, 2230, https://doi.org/10.1029/2001GL014342, 2002. 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 INCA, J. Geophys. Res., 109, D20206, https://doi.org/10.1029/2004JD004803, 2004. Gettelman, A., Fetzer, E. J., Eldering, A., and Irion, F. W.: The global distribution of supersaturation in the upper troposphere from the Atmospheric Infrared Sounder, J. Clim., 19, 6089–6103, 2006. Gierens, K., Schumann, U., Helten, M., Smit, H. G. J., 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. Goldfarb, L., Keckhut, P., Chanin, M.-L., and Hauchecorne, A.: Cirrus climatological results from Lidar measurements at OHP ($44^\circ$ N, $46^\circ$ {E}), Geophys. Res. Lett., 28, 1687–1690, 2001. Gu, Y. and Liou, K. N.: Cirrus cloud horizontal and vertical inhomogeneity effects in a GCM, Meteorol. Atmos. Phys., 91, 223–235, 2006. Heymsfield, A. J.: Properties of tropical and midlatitude ice cloud particle ensembles. Part&nbsp;II: Applications for mesoscale and climate models, J. Atmos. Sci., 60, 2592–2611, 2003. Heymsfield, A. J., Lawson, R. P., and Sachse, G. W.: Growth of ice crystals in a precipitating contrail, Geophys. Res. Lett., 25, 1335–1338, 1998. Heymsfield, A. J., Baumgardner, D., De{M}ott, P., Forster, P., Gierens, K., and Kärcher, B.: Contrail microphysics, Bull. Amer. Meteorol. Soc., 90, in press, 2009. Hogan, R. J. and Kew, S. F.: A 3-{D} stochastic cloud model for investigating the radiative properties of inhomogeneous cirrus clouds, Q. J. Roy. Meteorol. Soc., 131, 2585–2608, 2005. Immler, F. and Schrems, O.: Lidar measurements of cirrus clouds in the northern and southern midlatitudes during INCA ($55^\circ$ N, $53^\circ${S}): A comparative study, Geophys. Res. Lett., 29, 1809, https://doi.org/10.1029/2002GL015077, 2002. Immler, F., Treffeisen, R., Engelbart, D., Krüger, K., and Schrems, O.: Cirrus, contrails, and ice supersaturated regions in high pressure systems at northern midlatitudes, Atmos. Chem. Phys., 8, 1689–1699, 2008. Ivanova, D., Mitchell, D. L., Arnott, W. P., and Poellot, M.: A GCM parameteriztation for bimodal size spectra and ice mass removal rates in mid-latitude cirrus clouds, Atmos. Res., 59–60, 89–113, 2001. Jäger, H., Freudenthaler, V., and Homburg, F.: Remote sensing of optical depth of aerosols and clouds related to air traffic, Atmos. Environ., 32, 3123–3127, 1996. Jensen, E. J., Ackerman, A. S., Stevens, D. E., Toon, O. B., and Minnis, P.: Spreading and growth of contrails in a sheared environment, J. Geophys. Res., 103, 13557–13567, 1998. Jensen, E. J., Toon, O. B., Vay, S. A., Ovarlez, J., May, R., Bui, P., Twohy, C. H., Gandrud, B., Pueschel, R. F., and Schumann, U.: Prevalence of ice-supersaturated regions in the upper troposphere: Implications for optically thin ice cloud formation, J. Geophys. Res., 106, 17253–17266, 2001. Kärcher, B. and Solomon, S.: On the composition and optical extinction of particles in the tropopause region, J. Geophys. Res., 104, 27441–27459, 1999. Kärcher, B. and Ström, J.: The roles of dynamical variability and aerosols in cirrus cloud formation, Atmos. Chem. Phys., 3, 823–838, 2003. Kärcher, B. and Haag, W.: Factors controlling upper tropospheric relative humidity, Ann. Geophys., 22, 705–715, 2004. Kärcher, B. and Burkhardt, U.: A Cirrus cloud scheme for general circulation models, Q. J. Roy. Meteorol. Soc., 134, 1439–1461, 2008. Kärcher, B. and Yu, F.: The role of aircraft soot emissions in contrail formation, Geophys. Res. Lett., 36, L01804, https://doi.org/10.1029/2008GL036346, 2009. Kärcher, B. and Spichtinger, P.: Cloud-controlling factors of cirrus, in: Clouds in the {P}erturbed {C}limate {S}ystem: {T}heir {R}elationship to {E}nergy {B}alance, {A}tmospheric {D}ynamics, and {P}recipitation, edited by: Heintzenberg, J. and Charlson R. J., Strüngmann Forum Reports, vol.&nbsp;2, Cambridge, MA, MIT Press, 235–268, 2009. Kärcher, B., Mayer, B., Gierens, K., Burkhardt, U., Mannstein, H., and Chatterjee, R.: Aerodynamic contrails: Microphysics and optical properties, J. Atmos. Sci., 66, 227–243, 2009. Kästner, M., Kriebel, K. T., Renger, W., Ruppersberg, G. H., and Wendling, P.: Comparison of cirrus height and optical depth derived from satellite and aircraft measurements, Mon. Weather Rev., 121, 2708–2717, 1993. Kästner, M., Meyer, R., and Wendling, P.: Influence of weather conditions on the distribution of persistent contrails, Meteorol. Appl., 6, 261–271, 1999. Kay, J. E., Baker, M., and Hegg, D.: Microphysical and dynamical controls on cirrus cloud optical depth distributions, J. Geophys. Res., 111, D24205, https://doi.org/10.1029/2005JD006916, 2006. Khvorostyanov, V. and Sassen, K.: Cloud model simulation of a contrail case study: Surface cooling against upper tropospheric warming, Geophys. Res. Lett., 25, 2145–2148, 1998. Knollenberg, R. G.: Measurements of the growth of the ice budget in a persisting contrail, J. Atmos. Sci., 29, 1367–1374, 1972. Kosarev, A. L. and Mazin, I. P.: An empirical model of the physical structure of upper-layer clouds, Atmos. Res., 26, 213–228, 1991. Krebs, W., Mannstein, H., Bugliaro, L., and Mayer, B.: Technical note: A new day- and night-time M}eteosat {S}econd {G}eneration {C}irrus {D}etection {A}lgorithm {M}e{C}i{DA, Atmos. Chem. Phys., 7, 6145–6159, 2007. Lamquin, N., Stubenrauch, C. J., and Pelon, J.: Upper tropospheric humidity and cirrus geometrical and optical thicknesses: R}elationships inferred from 1 year of collocated {AIRS and CALIPSO data, J. Geophys. Res., 113, D00A08, https://doi.org/10.1029/2008JD010012, 2008. Lee, D. S., Fahey, D. W., Forster, P. M., Newton, P. J., Wit, R. C. N., Lim, L. L., Owen, B., and Sausen, R.: Aviation and global climate change in the $21^{\rm st}$ century, Atmos. Env., 43, 3520–3537, 2009. Lewellen, D. C. and Lewellen, W. S.: The effects of aircraft wake dynamics on contrail development, J. Atmos. Sci., 58, 390–406, 2001. Liou, K. N.: Influence of cirrus clouds on weather and climate processes: A global perspective, Mon. Weather Rev., 114, 1167–1199, 1986. Liou, K. N., Gu, Y., Yue, Q., and McFarquhar, G.: On the correlation between ice water content and ice crystal size and its application to radiative transfer and general circulation models, Geophys. Res. Lett., 35, L13805, https://doi.org/10.1029/2008GL033918, 2008. Mannstein, H., Meyer, R., and Wendling, P.: Operational detection of contrails from NOAA AVHRR data, Int. J. Remote Sens., 20, 1641–1660, 1999. Marquart, S.: Klimawirkung von Kondensstreifen: Untersuchungen mit einem globalen atmosphärischen Zirkulationsmodell, Doctoral Thesis (in German), Deutsches Zentrum f. Luft- u. Raumfahrt, DLR-FB 2003-16, 161&nbsp;pp., Cologne, Germany, 2003. Marquart, S., Ponater, M., Mager, F., and Sausen, R.: Future development of contrail cover, optical depth, and radiative forcing: {I}mpacts of increasing air traffic and climate change, J. Clim., 16, 2890–2904, 2003. Marti, J. and Mauersberger, K.: A survey and new measurements of ice vapor pressure at temperatures between 170 and 250&nbsp;{K}, Geophys. Res. Lett., 20, 363–366, 1993. Meyer, R.: Regionale Kondensstreifenbedeckung aus Satellitendaten und ihr Einfluss auf den Strahlungshaushalt, Doctoral Thesis (in German), Deutsches Zentrum f. Luft- u. Raumfahrt, DLR-FB 2000-26, 120&nbsp;pp., Cologne, Germany, 2000. Meyer, R., Mannstein, H., Meerkötter, R., Schumann, U., and Wendling, P.: Regional radiative forcing by line-shaped contrails derived from satellite data, J. Geophys. Res., 107, 4104, https://doi.org/10.1029/2001JD000426, 2002. Miloshevich, L. M. and Heymsfield, A. J.: A balloon-borne continuous cloud particle replicator for measuring vertical profiles of cloud microphysical properties: Instrument design, performance, and collection efficiency analysis, J. Atmos. Oceanic Technol., 14, 753–768, 1997. Minnis, P.: Contrails. I}n: <i>{E</i>ncyclopedia of {A}tmospheric {S}ciences, edited by: Holton, J., Pyle, J., and Curry, J., Academic Press, London, 509–520, 2003. Minnis, P., Young, D. F., Garber, D. P., Nguyen, L., Smith Jr., W. L., and Palikonda, R.: Transformation of contrails into cirrus during SUCCESS, Geophys. Res. Lett., 25, 1157–1160, 1998. Minnis, P., Palikonda, R., Walter, B. J., Ayers, J. K., and Mannstein, H.: Contrail properties over the eastern N}orth {P}acific from {AVHRR data, Meteorol. Z., 14, 515–523, 2005a. Minnis, P., Yi, Y., Huang, J., and Ayers, J. K.: Relationships between radiosonde and RUC}-2 meteorological conditions and cloud occurrence determined from {ARM data, J. Geophys. Res., 110, D23204, https://doi.org/10.1029/2005JD006005, 2005b. Mitchell, D. L.: Evolution of snow-size spectra in cyclonic storms. {P}art&nbsp;II: {D}eviations from the exponential form, J. Atmos. Sci., 48, 1885–1899, 1991. Mitchell, D. L.: Effective diameter in radiation transfer: {G}eneral definition, applications, and limitations, J. Atmos. Sci., 59, 2330–2346, 2002. Morrison, H. and Gettelman, A.: A new two-moment bulk stratiform cloud microphysics scheme in the {C}ommunity {A}tmosphere {M}odel, {V}ersion&nbsp;3 ({CAM}3). Part&nbsp;I: {D}escription and numerical tests, J. Clim., 21, 3642–3659, 2008. Palikonda, R., Minnis, P., Duda, D. P., and Mannstein, H.: Contrail coverage derived from AVHRR data over the continental {U}nited {S}tates of {A}merica and surrounding areas, Meteorol. Z., 14, 525–536, 2005. Poellot, M., Arnott, W., and Hallett, J.: In situ observations of contrail microphysics and implications for their radiative impact, J. Geophys. Res., 104, 12077–12084, 1999. Ponater, M., Marquart, S., and Sausen, R.: Contrails in a comprehensive global climate model: {P}arameterization and radiative forcing results, J. Geophys. Res., 107, 4164, https://doi.org/10.1029/2001JD000429, 2002. Pruppacher, H. R. and Klett, J. D.: \it Microphysics of {C}louds and {P}recipitation, Kluwer Acad., Norwell, Mass., 1997. Rädel, G., and Shine, K.: Evaluation of the use of radiosonde humidity data to predict the occurrence of persistent contrails, Q. J. Roy. Meteorol. Soc., 133, 1413–1424, 2007. Roskovensky, J. K. and Liou, K. N.: Detection of thin cirrus from 1.38 μm/0.65 μm reflectance ratio combined with $8.6{-}11 \mu$m brightness temperature difference, Geophys. Res. Lett., 30, 1985, https://doi.org/10.1029/2003GL018135, 2003. Rossow, W. B. and Schiffer, R. A.: Advances in understanding clouds from ISCCP, Bull. Amer. Meteorol. Soc., 80, 2261–2287, 1999. Sassen, K.: Contrail-cirrus and their potential for regional climate change, Bull. Amer. Meteorol. Soc., 78, 1885–1903, 1997. Sassen, K., and Cho, B. S.: Subvisual-thin cirrus Lidar data set for satellite verification and climatological research, J. Appl. Meteorol., 31, 1275–1285, 1992. Sausen, R., Isaksen, I., Grewe, V., Hauglustaine, D., Lee, D. S., Myhre, G., Köhler, M.O., Pitari, G., Schumann, U., Stordal, F., and Zerefos, C.: Aviation radiative forcing in 2000: An update on IPCC (1999), Meteorol. Z., 14, 555–561, 2005. Schiller, C., Krämer, M., Afchine, A., Spelten, N., and Sitnikov, N.: The ice water content of Arctic, midlatitude, and tropical cirrus, J. Geophys. Res., 113, D24208, https://doi.org/10.1029/2008JD010342, 2008. Schmitt, C. G., and Heymsfield, A. J.: The size distribution and mass-weighted terminal velocity of low-latitude tropopause cirrus crystal populations, J. Atmos. Sci., 66, 2013–2028, 2009. 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. Schumann, U.: On conditions for contrail formation from aircraft exhausts, Meteorol. Z., 5, 4–23, 1996. Schumann, U.: Contrail cirrus. In: Cirrus, edited by: Lynch, D. K., Sassen, K., Starr, D. O'C., and Stephens, G., Oxford Univ. Press, N.Y., 231–255, 2002. Schumann, U., Konopka, P., Baumann, R., Busen, R., Gerz, T., Schlager, H., Schulte, P., and Volkert, H.: Estimate of diffusion parameters of aircraft exhaust plumes near the tropopause from nitric oxide and turbulence measurements, J. Geophys. Res., 100, 14147–14162, 1995. Spichtinger, P., Gierens, K., Leiterer, U., and Dier, H.: Ice supersaturation in the tropopause region over Lindenberg, Germany, Meteorol. Z., 12, 143–156, 2003. Spichtinger, P. and Gierens, K. M.: Modelling of cirrus clouds – Part 1a: Model description and validation, Atmos. Chem. Phys., 9, 685–706, 2009. Spinhirne, J. D., Hart, W., and Duda, D. P.: Evolution of the morphology and microphysics of contrail cirrus from airborne remote sensing, Geophys. Res. Lett., 25, 1153–1156, 1998. Smith, W. L., Ackerman, S., Revercomb, H., Huang, H., De{S}lover, D. H., Feltz, W., Gumley, L., and Collard, A.: Infrared spectral absorption of nearly invisible cirrus clouds, Geophys. Res. Lett., 25, 1137–1140, 1998. Stephens, G. L.: Radiation profiles in extended water clouds. {II}: Parameterization schemes, J. Atmos. Sci., 35, 2123–2132, 1978. Stubenrauch, C. J., Eddounia, F., and Rädel, G.: Correlations between microphysical properties of large-scale semi-transparent cirrus and the state of the atmosphere, Atmos. Res., 72, 403–423, 2004. Stuefer, M., Meng, X., and Wendler, G.: MM5 contrail forecasting in {A}laska, Mon. Weather Rev., 133, 3517–3526, 2005. Sussmann, R.: Vertical dispersion of an aircraft wake: {A}erosol-lidar analysis of entrainment and detrainment in the vortex regime, J. Geophys. Res., 104, 2117–2129, 1999. Sussmann, R. and Gierens, K.: Differences in early contrail evolution of two-engine versus four-engine aircraft: Lidar measurements and numerical simulations, J. Geophys. Res., 106, 4899–4911, 2001. Treffeisen, R., Krejci, R., Ström, J., Engvall, A. C., Herber, A., and Thomason, L.: Humidity observations in the Arctic troposphere over Ny-Ålesund, Svalbard, based on 15 years of radiosonde data, Atmos. Chem. Phys., 7, 2721–2732, 2007. Unterstrasser, S., Gierens, K., and Spichtinger, P.: The evolution of contrail microphysics in the vortex phase, Meteorol. Z., 17, 145–156, 2008. Unterstrasser, S.: Numerische Simulationen von Kondensstreifen und deren Übergang in Zirren, Doctoral Thesis (in German), University of Munich, Department of Physics, 2008. Available from: <a href="http://edoc.ub.uni-muenchen.de/9464">http://edoc.ub.uni-muenchen.de/9464</a>, 2008. van de Hulst, H. C.: \it Light {S}cattering by {S}mall {P}articles, Wiley, New York, 1957. Wang, P. H., McCormick, M. P., Minnis, P., Kent, G. S., and Skeens, K. M.: A 6-year climatology of cloud occurrence frequency from SAGE&nbsp;II observations (1985-1990), J. Geophys. Res., 101, 29407–29429, 1996. Wang, Z. and Sassen, K.: Cirrus cloud microphysical property retrieval using lidar and radar measurements. Part&nbsp;{II}: Midlatitude microphysical and radiative properties, J. Atmos. Sci., 59, 2291–2302, 2002. Westbrook, C. D., Ball, R. C., Field, P. R., and Heymsfield, A. J.: Theory of growth by differential sedimentation with application to snowflake formation, Phys. Rev. E, 70, 021403-1–021403-7, 2004. Wylie, D., Piironen, P., Wolf, W., and Eloranta, E.: Understanding satellite cirrus cloud climatologies with calibrated lidar optical depths, J. Atmos. Sci., 52, 4327–4343, 1995.