• Anderson, B. E., W. R. Cofer, D. R. Bagwell, J. W. Barrick, C. H. Hudgins, and K. E. Brunke, 1998: Airborne observations of aircraft aerosol emissions I: Total nonvolatile particle emission indices. Geophys. Res. Lett., 25, 16891692, doi:10.1029/98GL00063.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Anderson, J. D., 2010: Fundamentals of Aerodynamics. McGraw Hill, 1106 pp.

  • Appleman, H., 1953: The formation of exhaust contrails by jet aircraft. Bull. Amer. Meteor. Soc., 34, 1420.

  • Atlas, D., and Z. Wang, 2010: Contrails of small and very large optical depth. J. Atmos. Sci., 67, 30653073, doi:10.1175/2010JAS3403.1.

  • Atlas, D., Z. Wang, and D. P. Duda, 2006: Contrails to cirrus—Morphology, microphysics, and radiative properties. J. Appl. Meteor. Climatol., 45, 519, doi:10.1175/JAM2325.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • aufm Kampe, H. J., 1943: Die Physik der Auspuffwolken hinter Flugzeugen (The physics of exhaust clouds behind aircraft). Luftwissen, 10, 171–173.

  • Bailey, M. P., and J. Hallett, 2009: A comprehensive habit diagram for atmospheric ice crystals: Confirmation from the laboratory, AIRS II, and other field studies. J. Atmos. Sci., 66, 28882899, doi:10.1175/2009JAS2883.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bauer, P., A. Thorpe, and G. Brunet, 2015: The quiet revolution of numerical weather prediction. Nature, 525, 4755, doi:10.1038/nature14956.

  • Baum, B. A., A. J. Heymsfield, P. Yang, and S. T. Bedka, 2005: Bulk scattering properties for the remote sensing of ice clouds. Part I: Microphysical data and models. J. Appl. Meteor., 44, 18851895, doi:10.1175/JAM2308.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Baumann, R., R. Busen, H. P. Fimpel, C. Kiemle, M. Reinhardt, and M. Quante, 1993: Measurements on contrails of commercial aircraft. Preprints, Eighth Symp. on Meteorological Observations and Instrumentation, Anaheim, CA, Amer. Meteor. Soc., 484–489.

  • Baumgardner, D., and W. A. Cooper, 1994: Airborne measurements in jet contrails: Characterization of the microphysical properties of aircraft wakes and exhausts. Impact of Emissions from Aircraft and Spacecraft upon the Atmosphere, U. Schumann, and D. Wurzel, Eds., DLR, 418–423.

  • Bedka, S. T., P. Minnis, D. P. Duda, T. L. Chee, and R. Palikonda, 2013: Properties of linear contrails in the Northern Hemisphere derived from 2006 Aqua MODIS observations. Geophys. Res. Lett., 40, 772777, doi:10.1029/2012GL054363.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Birner, T., A. Dörnbrack, and U. Schumann, 2002: How sharp is the tropopause at midlatitudes? Geophys. Res. Lett., 29, 45-1–45-4, doi:10.1029/2002gl015142.

    • Crossref
    • Export Citation
  • Bock, L., and U. Burkhardt, 2016a: The temporal evolution of a long-lived contrail cirrus cluster: Simulations with a global climate model. J. Geophys. Res. Atmos., 121, 35483565, doi:10.1002/2015JD024475.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bock, L., and U. Burkhardt, 2016b: Reassessing properties and radiative forcing of contrail cirrus using a climate model. J. Geophys. Res. Atmos, 121, 97179736, doi:10.1002/2016JD025112.

    • Search Google Scholar
    • Export Citation
  • Boies, A. M., and et al. , 2015: Particle emission characteristics of a gas turbine with a double annular combustor. Aerosol Sci. Technol., 49, 842855, doi:10.1080/02786826.2015.1078452.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bond, T. C., and et al. , 2013: Bounding the role of black carbon in the climate system: A scientific assessment. J. Geophys. Res. Atmos., 118, 53805552, doi:10.1002/jgrd.50171.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Boucher, O., and et al. , 2013: Clouds and aerosols. Climate Change 2013: The Physical Science Basis, T. F. Stocker, et al., Eds., Cambridge University Press, 571–657.

  • Brasseur, G. P., and et al. , 2016: Impact of aviation on climate: FAA’s Aviation Climate Change Research Initiative (ACCRI) Phase II. Bull. Amer. Meteor. Soc., 97, 561583, doi:10.1175/BAMS-D-13-00089.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Braun-Unkhoff, M., and U. Riedel, 2015: Alternative fuels in aviation. CEAS Aeronaut. J., 6, 8393, doi:10.1007/s13272-014-0131-2.

  • Brewer, A. W., 1946: Condensation trails. Weather, 1, 3440, doi:10.1002/j.1477-8696.1946.tb00024.x.

  • Brewer, A. W., 2000: The stratospheric circulation: A personal history. SPARC Newsletter, No. 15, 28–32. [Available online at http://www.atmosp.physics.utoronto.ca/SPARC/News15/15_Norton.html.]

  • Brock, C. A., F. Schröder, B. Kärcher, A. Petzold, R. Busen, and M. Fiebig, 2000: Ultrafine particle size distributions measured in aircraft exhaust plumes. J. Geophys. Res., 105, 26 55526 567, doi:10.1029/2000JD900360.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Burkhardt, U., and B. Kärcher, 2011: Global radiative forcing from contrail cirrus. Nat. Climate Change, 1, 5458, doi:10.1038/nclimate1068.

  • Burkhardt, U., B. Kärcher, M. Ponater, K. Gierens, and A. Gettelman, 2008: Contrail cirrus supporting areas in model and observations. Geophys. Res. Lett., 35, L16808, doi:10.1029/2008GL034056.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Busen, R., and U. Schumann, 1995: Visible contrail formation from fuels with different sulfur contents. Geophys. Res. Lett., 22, 13571360, doi:10.1029/95GL01312.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, C.-C., and A. Gettelman, 2013: Simulated radiative forcing from contrails and contrail cirrus. Atmos. Chem. Phys., 13, 12 52512 536, doi:10.5194/acp-13-12525-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Comstock, J. M., T. P. Ackerman, and D. D. Turner, 2004: Evidence of high ice supersaturation in cirrus clouds using ARM Raman lidar measurements. Geophys. Res. Lett., 31, L11106, doi:10.1029/2004GL019705.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • de Bruin, A., and H. Kannemans, 2004: Analysis of NLR Cessna Citation flight test data for flight test-1 in AWIATOR project. NLR Tech. Rep. AW-NLR-113-010, 101 pp.

  • De Leon, R. R., M. Krämer, D. S. Lee, and J. C. Thelen, 2012: Sensitivity of radiative properties of persistent contrails to the ice water path. Atmos. Chem. Phys., 12, 78937901, doi:10.5194/acp-12-7893-2012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Delisi, D. P., and R. E. Robins, 2000: Short-scale instabilities in trailing wake vortices in a stratified fluid. AIAA J., 38, 19161923, doi:10.2514/2.845.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Delisi, D. P., and G. C. Greene, 2009: Experimental measurements of the evolution of a vortex pair in a nonstratified fluid. Part 1: Migration and persistence. Proc. 47th AIAA Aerospace Sciences Meeting, Orlando, FL, AIAA, 14, doi:10.2514/6.2009-345.

    • Crossref
    • Export Citation
  • De Visscher, I., L. Bricteux, and G. Winckelmans, 2013: Aircraft vortices in stably stratified and weakly turbulent atmospheres: Simulation and modeling. AIAA J., 51, 551566, doi:10.2514/1.J051742.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dickson, N. C., K. M. Gierens, H. L. Rogers, and R. L. Jones, 2010: Probabilistic description of ice-supersaturated layers in low resolution profiles of relative humidity. Atmos. Chem. Phys., 10, 67496763, doi:10.5194/acp-10-6749-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dietmüller, S., and et al. , 2016: A new radiation infrastructure for the Modular Earth Submodel System (MESSy, based on version 2.51). Geosci. Model Dev., 9, 2209–2222, doi:10.5194/gmd-9-2209-2016.

    • Crossref
    • Export Citation
  • Duda, D. P., and P. Minnis, 2002: Observations of aircraft dissipation trails from GOES. Mon. Wea. Rev., 130, 398406, doi:10.1175/1520-0493(2002)130<0398:OOADTF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Duda, D. P., P. Minnis, and L. Nguyen, 2001: Estimates of cloud radiative forcing in contrail clusters using GOES imagery. J. Geophys. Res., 106, 49274937, doi:10.1029/2000JD900393.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Duda, D. P., P. Minnis, L. Nyuyen, and R. Palikonda, 2004: A case study of the development of contrail clusters over the Great Lakes. J. Atmos. Sci., 61, 11321146, doi:10.1175/1520-0469(2004)061<1132:ACSOTD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Duda, D. P., P. Minnis, K. Khlopenkov, T. L. Chee, and R. Boeke, 2013: Estimation of 2006 Northern Hemisphere contrail coverage using MODIS data. Geophys. Res. Lett., 40, 612–617, doi:10.1002/grl.50097.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Duda, D. P., T. Chee, K. Khlopenkov, S. Bedka, and P. Minnis, 2015: Linear contrail coverage and cloud property retrievals from 2012 MODIS imagery over the Northern Hemisphere. 2015 Fall Meeting, San Francisco, CA, Amer. Geophys. Union., Abstract A11S-03.

  • Dyroff, C., A. Zahn, E. Christner, R. M. Forbes, A. M. Tompkins, and P. J. van Velthoven, 2015: Comparison of ECMWF analysis and forecast humidity data with CARIBIC upper troposphere and lower stratosphere observations. Quart. J. Roy. Meteor. Soc., 141A, 833844, doi:10.1002/qj.2400.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ewald, F., L. Bugliaro, H. Mannstein, and B. Mayer, 2013: An improved cirrus detection algorithm MeCiDA2 for SEVIRI and its evaluation with MODIS. Atmos. Meas. Tech., 6, 309322, doi:10.5194/amt-6-309-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fahey, D. W., and et al. , 1995: Emission measurements of the Concorde supersonic aircraft in the lower stratosphere. Science, 270, 7074, doi:10.1126/science.270.5233.70.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Febvre, G., and et al. , 2009: On optical and microphysical characteristics of contrails and cirrus. J. Geophys. Res., 114, D02204, doi:10.1029/2008JD010184.

    • Search Google Scholar
    • Export Citation
  • Freudenthaler, V., F. Homburg, and H. Jäger, 1995: Contrail observations by ground-based scanning lidar: Cross-sectional growth. Geophys. Res. Lett., 22, 35013504, doi:10.1029/95GL03549.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Freudenthaler, V., F. Homburg, and H. Jäger, 1996: Optical parameters of contrails from lidar measurements: Linear depolarization. Geophys. Res. Lett., 23, 37153718, doi:10.1029/96GL03646.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frömming, C., M. Ponater, U. Burkhardt, A. Stenke, S. Pechtl, and R. Sausen, 2011: Sensitivity of contrail coverage and contrail radiative forcing to selected key parameters. Atmos. Environ., 45, 14831490, doi:10.1016/j.atmosenv.2010.11.033.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fuglestvedt, J. S., and et al. , 2010: Transport impacts on atmosphere and climate: Metrics. Atmos. Environ., 44, 46484677, doi:10.1016/j.atmosenv.2009.04.044.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, R. C., and et al. , 2006: Measurements of relative humidity in a persistent contrail. Atmos. Environ., 40, 15901600, doi:10.1016/j.atmosenv.2005.11.021.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gayet, J.-F., G. Febvre, G. Brogniez, H. Chepfer, W. Renger, and P. Wendling, 1996: Microphysical and optical properties of cirrus and contrails. J. Atmos. Sci., 53, 126138, doi:10.1175/1520-0469(1996)053<0126:MAOPOC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gayet, J.-F., and et al. , 2012: The evolution of microphysical and optical properties of an A380 contrail in the vortex phase. Atmos. Chem. Phys., 12, 66296643, doi:10.5194/acp-12-6629-2012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gerz, T., and T. Ehret, 1996: Wake dynamics and exhaust distribution behind cruising aircraft. AGARD Fluid Dynamics Panel Meeting and Symp. on the Characterization and Modification of Wakes from Lifting Vehicles in Fluids, Trondheim, Norway, AGARD CP 584, 35.31–35.38.

  • Gerz, T., and F. Holzäpfel, 1999: Wing tip vortices, turbulence and the distribution of emissions. AIAA J., 37, 12701276, doi:10.2514/2.595.

  • Gettelman, A., and C. Chen, 2013: The climate impact of aviation aerosols. Geophys. Res. Lett., 40, 2785–2789, doi:10.1002/grl.50520.

  • Gierens, K., 2012: Selected topics on the interaction between cirrus clouds and embedded contrails. Atmos. Chem. Phys., 12, 11 94311 949, doi:10.5194/acp-12-11943-2012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gierens, K., and P. Spichtinger, 2000: On the size distribution of ice-supersaturated regions in the upper troposphere and lowermost stratosphere. Ann. Geophys., 18, 499504, doi:10.1007/s00585-000-0499-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gierens, K., and S. Brinkop, 2012: Dynamical characteristics of ice supersaturated regions. Atmos. Chem. Phys., 12, 11 93311 942, doi:10.5194/acp-12-11933-2012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gierens, K., and F. Dilger, 2013: A climatology of formation conditions for aerodynamic contrails. Atmos. Chem. Phys., 13, 10 847–10 857, doi:10.5194/acp-13-10847-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gierens, K., B. Kärcher, H. Mannstein, and B. Mayer, 2009: Aerodynamic contrails: Phenomenology and flow physics. J. Atmos. Sci., 66, 217226, doi:10.1175/2008JAS2767.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gierens, K., M. Kästner, and D. Klatt, 2011: Iridescent aerodynamic contrails: The Norderney case of 27 June 2008. Meteor. Z., 20, 305311, doi:10.1127/0941-2948/2011/0497.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gierens, K., P. Spichtinger, and U. Schumann, 2012: Ice supersaturation. Atmospheric Physics: Background—Methods—Trends, U. Schumann, Ed., Research Topics in Aerospace Series, Vol. 1, Springer, 135–150, doi:10.1007/978-3-642-30183-4_9.

    • Crossref
    • Export Citation
  • Graf, K., U. Schumann, H. Mannstein, and B. Mayer, 2012: Aviation induced diurnal North Atlantic cirrus cover cycle. Geophys. Res. Lett., 39, L16804, doi:10.1029/2012GL052590.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Greene, G. C., 1986: An approximate model of wake vortex decay in the atmosphere. J. Aircr., 23, 566573, doi:10.2514/3.45345.

  • Grewe, V., T. Champougny, S. Matthes, C. Frömming, S. Brinkop, O. A. Søvde, E. A. Irvine, and L. Halscheidt, 2014a: Reduction of the air traffic’s contribution to climate change: A REACT4C case study. Atmos. Environ., 94, 616625, doi:10.1016/j.atmosenv.2014.05.059.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grewe, V., and et al. , 2014b: Aircraft routing with minimal climate impact: The REACT4C climate cost function modelling approach (V1.0). Geosci. Model Dev., 7, 175201, doi:10.5194/gmd-7-175-2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hansen, J. E., and L. D. Travis, 1974: Light scattering in planetary atmospheres. Space Sci. Rev., 16, 527610, doi:10.1007/BF00168069.

  • Hansen, J. E., and et al. , 2005: Efficacy of climate forcings. J. Geophys. Res., 110, D18104, doi:10.1029/2005JD005776.

  • Haywood, J. M., and et al. , 2009: A case study of the radiative forcing of persistent contrails evolving into contrail-induced cirrus. J. Geophys. Res., 114, D24201, doi:10.1029/2009JD012650.

    • Search Google Scholar
    • Export Citation
  • Helten, M., and et al. , 1999: In-flight comparison of MOZAIC and POLINAT water vapor measurements. J. Geophys. Res., 104, 26 08726 096, doi:10.1029/1999JD900315.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hendricks, J., B. Kärcher, and U. Lohmann, 2011: Effects of ice nuclei on cirrus clouds in a global climate model. J. Geophys. Res., 116, D18206, doi:10.1029/2010JD015302.

    • Search Google Scholar
    • Export Citation
  • Hennemann, I., and F. Holzäpfel, 2011: Large-eddy simulation of aircraft wake vortex deformation and topology. J. Aerosp. Eng., 25, 13361350, doi:10.1177/0954410011402257.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., R. P. Lawson, and G. W. Sachse, 1998: Growth of ice crystals in a precipitating contrail. Geophys. Res. Lett., 25, 13351338, doi:10.1029/98GL00189.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., D. Baumgardner, P. DeMott, P. Forster, K. Gierens, and B. Kärcher, 2010: Contrail microphysics. Bull. Amer. Meteor. Soc., 91, 465472, doi:10.1175/2009BAMS2839.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., G. Thompson, H. Morrison, A. Bansemer, R. M. Rasmussen, P. Minnis, Z. Wang, and D. Zhang, 2011: Formation and spread of aircraft-Induced holes in clouds. Science, 333, doi:10.1126/science.1202851.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., C. Schmitt, and A. Bansemer, 2013: Ice cloud particle size distributions and pressure-dependent terminal velocities from in situ observations at temperatures from 0° to −86°C. J. Atmos. Sci., 70, 41234154, doi:10.1175/JAS-D-12-0124.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holzäpfel, F., 2003: Probabilistic two-phase wake vortex decay and transport model. J. Aircr., 40, 323331, doi:10.2514/2.3096.

  • Holzäpfel, F., 2014: Effects of environmental and aircraft parameters on wake vortex behavior. J. Aircr., 51, 14901500, doi:10.2514/1.C032366.

  • Hoshizaki, H., L. B. Anderson, R. J. Conti, N. Farlow, J. W. Meyer, T. Overcamp, K. O. Redler, and V. Watson, 1975: Aircraft wake microscale phenomena. The Stratosphere Perturbed by Propulsion Effluents, A. J. Grobecker, Ed., Department of Transportation, Climatic Impact Assessment Program, 2-1–2-79.

  • Immler, F., R. Treffeisen, D. Engelbart, K. Krüger, and O. Schrems, 2008: Cirrus, contrails, and ice supersaturated regions in high pressure systems at northern mid latitudes. Atmos. Chem. Phys., 8, 16891699, doi:10.5194/acp-8-1689-2008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • IPCC, 2013: Climate Change 2013: The Physical Science Basis. Cambridge University Press, 1535 pp.

  • Irvine, E. A., and K. P. Shine, 2015: Ice supersaturation and the potential for contrail formation in a changing climate. Earth Syst. Dyn., 6, 555568, doi:10.5194/esd-6-555-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Iwabuchi, H., P. Yang, K. N. Liou, and P. Minnis, 2012: Physical and optical properties of persistent contrails: Climatology and interpretation. J. Geophys. Res., 117, D06215, doi:10.1029/2011JD017020.

    • Search Google Scholar
    • Export Citation
  • Jansen, J., and A. J. Heymsfield, 2015: Microphysics of aerodynamic contrail formation processes. J. Atmos. Sci., 72, 32933308, doi:10.1175/JAS-D-14-0362.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jensen, E. J., and O. B. Toon, 1997: The potential impact of soot particles from aircraft exhaust on cirrus clouds. Geophys. Res. Lett., 24, 249252, doi:10.1029/96GL03235.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jensen, E. J., A. S. Ackermann, D. E. Stevens, O. B. Toon, and P. Minnis, 1998a: Spreading and growth of contrails in a sheared environment. J. Geophys. Res., 103, 13 557–513 567, doi:10.1029/98JD02594.

    • Crossref
    • Export Citation
  • Jensen, E. J., and et al. , 1998b: Environmental conditions required for contrail formation and persistence. J. Geophys. Res., 103, 39293936, doi:10.1029/97JD02808.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jensen, E. J., and et al. , 2001: Prevalence of ice-supersaturated regions in the upper troposphere: Implications for optically thin ice cloud formation. J. Geophys. Res., 106, 17 25317 266, doi:10.1029/2000JD900526.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jeßberger, P., and et al. , 2013: Aircraft type influence on contrail properties. Atmos. Chem. Phys., 13, 11 96511 984, doi:10.5194/acp-13-11965-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, H. M., and et al. , 2012: A methodology for in-situ and remote sensing of microphysical and radiative properties of contrails as they evolve into cirrus. Atmos. Chem. Phys., 12, 81578175, doi:10.5194/acp-12-8157-2012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jurkat, T., and et al. , 2011: Measurements of HONO, NO, NOy and SO2 in aircraft exhaust plumes at cruise. Geophys. Res. Lett., 38, L10807, doi:10.1029/2011GL046884.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kärcher, B., and F. Yu, 2009: Role of aircraft soot emissions in contrail formation. Geophys. Res. Lett., 36, L01804, doi:10.1029/2008GL036649.

  • Kärcher, B., and U. Burkhardt, 2013: Effects of optical depth variability on contrail radiative forcing. Quart. J. Roy. Meteor. Soc., 139, 16581664, doi:10.1002/qj.2053.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kärcher, B., T. Peter, U. M. Biermann, and U. Schumann, 1996: The initial composition of jet condensation trails. J. Atmos. Sci., 53, 30663083, doi:10.1175/1520-0469(1996)053<3066:TICOJC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kärcher, B., B. Mayer, K. Gierens, U. Burkhardt, H. Mannstein, and R. Chatterjee, 2009: Aerodynamic contrails: Microphysics and optical properties. J. Atmos. Sci., 66, 227243, doi:10.1175/2008JAS2768.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kärcher, B., U. Burkhardt, A. Bier, L. Bock, and I. J. Ford, 2015: The microphysical pathway to contrail formation. J. Geophys. Res. Atmos., 120, 78937927, doi:10.1002/2015JD023491.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaufmann, S., C. Voigt, P. Jeßberger, T. Jurkat, H. Schlager, A. Schwarzenboeck, M. Klingebiel, and T. Thornberry, 2014: In-situ measurements of ice saturation in young contrails. Geophys. Res. Lett., 41, 702709, doi:10.1002/2013GL058276.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Khou, J.-C., W. Ghedhaifi, X. Vancassel, and F. Garnier, 2015: Spatial simulation of contrail formation in near-field of commercial aircraft. J. Aircr., 52, 19271938, doi:10.2514/1.C033101.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Khvorostyanov, V., and K. Sassen, 1998: Cloud model simulation of a contrail case study: Surface cooling against upper tropospheric warming. Geophys. Res. Lett., 25, 21452148, doi:10.1029/98GL01522.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kienast-Sjögren, E., P. Spichtinger, and K. Gierens, 2013: Formulation and test of an ice aggregation scheme for two-moment bulk microphysics schemes. Atmos. Chem. Phys., 13, 90219037, doi:10.5194/acp-13-9021-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Knollenberg, R. G., 1972: Measurements of the growth of the ice budget in a persisting contrail. J. Atmos. Sci., 29, 13671374, doi:10.1175/1520-0469(1972)029<1367:MOTGOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Koehler, K. A., and et al. , 2009: Cloud condensation nuclei and ice nucleation activity of hydrophobic and hydrophilic soot particles. Phys. Chem. Chem. Phys., 11, 79067920, doi:10.1039/b905334b.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Konopka, P., 1995: Analytical Gaussian solutions for anisotropic diffusion in a linear shear flow. J. Non-Equilib. Thermodyn., 20, 78–91.

    • Crossref
    • Export Citation
  • Korolev, A., and I. P. Mazin, 2003: Supersaturation of water vapor in clouds. J. Atmos. Sci., 60, 29572974, doi:10.1175/1520-0469(2003)060<2957:SOWVIC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Korolev, A., E. Emery, J. Strapp, S. Cober, G. Isaac, M. Wasey, and D. Marcotte, 2011: Small ice particles in tropospheric clouds: Fact or artifact? Airborne icing instrumentation evaluation experiment. Bull. Amer. Meteor. Soc., 92, 967973, doi:10.1175/2010BAMS3141.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kristensson, A., J.-F. Gayet, J. Ström, and F. Auriol, 2000: In situ observations of a reduction in effective crystal diameter in cirrus clouds near flight corridors. Geophys. Res. Lett., 27, 681684, doi:10.1029/1999GL010934.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuhn, M., A. Petzold, D. Baumgardner, and F. Schröder, 1998: Particle composition of a young condensation trail and of upper tropospheric aerosol. Geophys. Res. Lett., 25, 26792682, doi:10.1029/98GL01932.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Laken, B. A., E. Palla, D. R. Kniveton, C. J. R. Williams, and D. A. Kilham, 2012: Contrails developed under frontal influences of the North Atlantic. J. Geophys. Res., 117, D11201, doi:10.1029/2011JD017019.

    • Search Google Scholar
    • Export Citation
  • Lamquin, N., C. J. Stubenrauch, K. Gierens, U. Burkhardt, and H. Smit, 2012: A global climatology of upper-tropospheric ice supersaturation occurrence inferred from the Atmospheric Infrared Sounder calibrated by MOZAIC. Atmos. Chem. Phys., 12, 381405, doi:10.5194/acp-12-381-2012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, D. S., and et al. , 2010: Transport impacts on atmosphere and climate: Aviation. Atmos. Environ., 44, 46784734, doi:10.1016/j.atmosenv.2009.06.005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lewellen, D. C., 2012: Analytic solutions for evolving size distributions of spherical crystals or droplets undergoing diffusional growth in different regimes. J. Atmos. Sci., 69, 417434, doi:10.1175/JAS-D-11-029.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lewellen, D. C., 2014: Persistent contrails and contrail cirrus. Part II: Full lifetime behavior. J. Atmos. Sci., 71, 44204438, doi:10.1175/JAS-D-13-0317.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lewellen, D. C., and W. S. Lewellen, 2001: The effects of aircraft wake dynamics on contrail development. J. Atmos. Sci., 58, 390406, doi:10.1175/1520-0469(2001)058<0390:TEOAWD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lewellen, D. C., O. Meza, and W. W. Huebsch, 2014: Persistent contrails and contrail cirrus. Part I: Large-eddy simulations from inception to demise. J. Atmos. Sci., 71, 43994419, doi:10.1175/JAS-D-13-0316.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liou, K. N., S. C. Ou, and G. Koenig, 1990: An investigation of the climatic effect of contrail cirrus. Air Traffic and the Environment—Background, Tendencies and Potential Global Atmospheric Effects, U. Schumann, Ed., Lecture Notes in Engineering, Springer, 154–169.

    • Crossref
    • Export Citation
  • Liu, X., J. E. Penner, S. J. Ghan, and M. Wang, 2007: Inclusion of ice microphysics in the NCAR Community Atmospheric Model version 3 (CAM3). J. Climate, 20, 45264547, doi:10.1175/JCLI4264.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lohmann, U., P. Spichtinger, S. Jess, T. Peter, and H. Smit, 2008: Cirrus cloud formation and ice supersaturated regions in a global climate model. Environ. Res. Lett., 3, 045022, doi:10.1088/1748-9326/3/4/045022.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mannstein, H., R. Meyer, and P. Wendling, 1999: Operational detection of contrails from NOAA-AVHRR data. Int. J. Remote Sens., 20, 16411660, doi:10.1080/014311699212650.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mannstein, H., A. Brömser, and L. Bugliaro, 2010: Ground-based observations for the validation of contrails and cirrus detection in satellite imagery. Atmos. Meas. Tech., 3, 655669, doi:10.5194/amt-3-655-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Markowicz, K. M., and M. L. Witek, 2011: Simulations of contrail optical properties and radiative forcing for various crystal shapes. J. Appl. Meteor. Climatol., 50, 17401755, doi:10.1175/2011JAMC2618.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marquart, S., M. Ponater, F. Mager, and R. Sausen, 2003: Future development of contrail cover, optical depth and radiative forcing: Impacts of increasing air traffic and climate change. J. Climate, 16, 28902904, doi:10.1175/1520-0442(2003)016<2890:FDOCCO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mayer, B., and A. Kylling, 2005: The libRadtran software package for radiative transfer calculations: Description and examples of use. Atmos. Chem. Phys., 5, 18551877, doi:10.5194/acp-5-1855-2005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Meerkötter, R., U. Schumann, P. Minnis, D. R. Doelling, T. Nakajima, and Y. Tsushima, 1999: Radiative forcing by contrails. Ann. Geophys., 17, 10801094, doi:10.1007/s00585-999-1080-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Minnis, P., D. F. Young, D. P. Garber, L. Nguyen, W. L. Smith Jr., and R. Palikonda, 1998: Transformation of contrails into cirrus during SUCCESS. Geophys. Res. Lett., 25, 11571160, doi:10.1029/97GL03314.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Minnis, P., J. K. Ayers, M. L. Nordeen, and S. P. Weaver, 2003: Contrail frequency over the United States from surface observations. J. Climate, 16, 34473462, doi:10.1175/1520-0442(2003)016<3447:CFOTUS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Minnis, P., J. K. Ayers, R. Palikonda, and D. Phan, 2004: Contrails, cirrus trends, and climate. J. Climate, 17, 16711685, doi:10.1175/1520-0442(2004)017<1671:CCTAC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Minnis, P., and et al. , 2013: Linear contrail and contrail cirrus properties determined from satellite data. Geophys. Res. Lett., 40, 32203226, doi:10.1002/grl.50569.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Misaka, T., F. Holzäpfel, I. Hennemann, T. Gerz, M. Manhart, and F. Schwertfirm, 2012: Vortex bursting and tracer transport of a counter-rotating vortex pair. Phys. Fluids, 24, 025104, doi:10.1063/1.3684990.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Misaka, T., F. Holzäpfel, and T. Gerz, 2015: Large-eddy simulation of aircraft wake evolution from roll-up until vortex decay. AIAA J., 53, 26462670, doi:10.2514/1.J053671.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moore, R. H., and et al. , 2015: Influence of jet fuel composition on aircraft engine emissions: A synthesis of aerosol emissions data from the NASA APEX, AAFEX, and ACCESS missions. Energy Fuels, 29, 25912600, doi:10.1021/ef502618w.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Myhre, G., and et al. , 2009: Intercomparison of radiative forcing calculations of stratospheric water vapour and contrails. Meteor. Z., 18, 585596, doi:10.1127/0941-2948/2009/0411.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Naiman, A. D., S. K. Lele, and M. Z. Jacobson, 2011: Large eddy simulations of contrail development: Sensitivity to initial and ambient conditions over first twenty minutes. J. Geophys. Res., 116, D21208, doi:10.1029/2011JD015806.

    • Search Google Scholar
    • Export Citation
  • Ovarlez, J., P. van Velthoven, G. Sachse, S. Vay, H. Schlager, and H. Ovarlez, 2000: Comparison of water vapor measurements from POLINAT2 with ECMWF analyses in high humidity conditions. J. Geophys. Res., 105, 37373744, doi:10.1029/1999JD900954.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ovarlez, J., J. F. Gayet, K. Gierens, J. Ström, H. Ovarlez, F. Auriol, R. Busen, and U. Schumann, 2002: Water vapor measurements inside cirrus clouds in northern and southern hemispheres during INCA. Geophys. Res. Lett., 29, 60-1–60-4, doi:10.1029/2001gl014440.

    • Crossref
    • Export Citation
  • Paoli, R., and K. Shariff, 2016: Contrail modeling and simulation. Annu. Rev. Fluid Mech., 48, 393427, doi:10.1146/annurev-fluid-010814-013619.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Paoli, R., L. Nybelen, J. Picot, and D. Cariolle, 2013: Effects of jet/vortex interaction on contrail formation in supersaturated conditions. Phys. Fluids, 25, 053305, doi:10.1063/1.4807063.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Paoli, R., O. Thouron, J. Escobar, J. Picot, and D. Cariolle, 2014: High-resolution large-eddy simulations of stably stratified flows: Application to subkilometer-scale turbulence in the upper troposphere–lower stratosphere. Atmos. Chem. Phys., 14, 50375055, doi:10.5194/acp-14-5037-2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peck, J., O. O. Oluwole, H.-W. Wong, and R. C. Miake-Lye, 2013: An algorithm to estimate aircraft cruise black carbon emissions for use in developing a cruise emissions inventory. J. Air Waste Manage. Assoc., 63, 367375, doi:10.1080/10962247.2012.751467.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pedgley, D. E., 2008: Some thoughts on fallstreak holes. Weather, 63, 356360, doi:10.1002/wea.279.

  • Penner, J. E., D. H. Lister, D. J. Griggs, D. J. Dokken, and M. McFarland, Eds., 1999: Aviation and the Global Atmosphere. Cambridge University Press, 373 pp.

  • Penner, J. E., Y. Chen, M. Wang, and X. Liu, 2009: Possible influence of anthropogenic aerosols on cirrus clouds and anthropogenic forcing. Atmos. Chem. Phys., 9, 879896, doi:10.5194/acp-9-879-2009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Petzold, A., and et al. , 1997: Near-field measurements on contrail properties from fuels with different sulfur content. J. Geophys. Res., 102, 29 86729 880, doi:10.1029/97JD02209.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Petzold, A., and et al. , 2013: Recommendations for reporting “black carbon” measurements. Atmos. Chem. Phys., 13, 83658379, doi:10.5194/acp-13-8365-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Petzold, A., A. Döpelheuer, C. A. Brock, and F. Schröder, 1999: In situ observation and model calculations of black carbon emission by aircraft at cruise altitude. J. Geophys. Res., 104, 22 17122 181, doi:10.1029/1999JD900460.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Picot, J., R. Paoli, O. Thouron, and D. Cariolle, 2015: Large-eddy simulation of contrail evolution in the vortex phase and its interaction with atmospheric turbulence. Atmos. Chem. Phys., 15, 73697389, doi:10.5194/acp-15-7369-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Poellot, M. R., W. P. Arnott, and J. Hallett, 1999: In situ observations of contrail microphysics and implications for their radiative impact. J. Geophys. Res., 104, 12 07712 084, doi:10.1029/1999JD900109.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ponater, M., S. Marquart, and R. Sausen, 2002: Contrails in a comprehensive global climate model: Parameterization and radiative forcing results. J. Geophys. Res., 107, 4164, doi:10.1029/2001JD000429.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ponater, M., S. Marquart, R. Sausen, and U. Schumann, 2005: On contrail climate sensitivity. Geophys. Res. Lett., 32, L10706, doi:10.1029/2005GL022580.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rap, A., P. M. Forster, J. M. Haywood, A. Jones, and O. Boucher, 2010a: Estimating the climate impact of linear contrails using the UK Met Office climate model. Geophys. Res. Lett., 37, L20703, doi:10.1029/2010GL045161.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rap, A., P. M. Forster, A. Jones, O. Boucher, J. M. Haywood, N. Bellouin, and R. R. D. Leon, 2010b: Parameterization of contrails in the UK Met Office Climate Model. J. Geophys. Res., 115, D10205, doi:10.1029/2009JD012443.

    • Search Google Scholar
    • Export Citation
  • Rojo, C., X. Vancassel, P. Mirabel, J.-L. Ponche, and F. Garnier, 2015: Impact of alternative jet fuels on aircraft-induced aerosols. Fuels, 144, 335341, doi:10.1016/j.fuel.2014.12.021.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ryan, A. C., A. R. MacKenzie, S. Watkins, and R. Timmis, 2011: World War II contrails: A case study of aviation-induced cloudiness. Int. J. Climatol., 32, 1745–1753, doi:10.1002/joc.2392.

    • Search Google Scholar
    • Export Citation
  • Sarpkaya, T., 1983: Trailing vortices in homogeneous and density stratified media. J. Fluid Mech., 136, 85109, doi:10.1017/S0022112083002074.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sassen, K., 1979: Iridescence in an aircraft contrail. J. Opt. Soc. Amer., 69, 10801083, doi:10.1364/JOSA.69.001080.

  • Sausen, R., K. Gierens, M. Ponater, and U. Schumann, 1998: A diagnostic study of the global distribution of contrails. Part I: Present day climate. Theor. Appl. Climatol., 61, 127141, doi:10.1007/s007040050058.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schäuble, D., and et al. , 2009: Airborne measurements of the nitric acid partitioning in persistent contrails. Atmos. Chem. Phys., 9, 81898197, doi:10.5194/acp-9-8189-2009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schröder, F. P., B. Kärcher, A. Petzold, R. Baumann, R. Busen, C. Hoell, and U. Schumann, 1998: Ultrafine aerosol particles in aircraft plumes: In situ observations. Geophys. Res. Lett., 25, 27892792, doi:10.1029/98GL02078.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schröder, F. P., and et al. , 2000: The transition of contrails into cirrus clouds. J. Atmos. Sci., 57, 464480, doi:10.1175/1520-0469(2000)057<0464:OTTOCI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., 1996: On conditions for contrail formation from aircraft exhausts. Meteor. Z., 5, 423.

  • Schumann, U., 2002: Contrail cirrus. Cirrus, D. K. Lynch et al., Eds., Oxford University Press, 231–255.

    • Crossref
    • Export Citation
  • Schumann, U., 2005: Formation, properties and climate effects of contrails. C. R. Phys., 6, 549565, doi:10.1016/j.crhy.2005.05.002.

  • Schumann, U., 2012: A contrail cirrus prediction model. Geosci. Model Dev., 5, 543580, doi:10.5194/gmd-5-543-2012.

  • Schumann, U., and P. Wendling, 1990: Determination of contrails from satellite data and observational results. Air Traffic and the Environment—Background, Tendencies and Potential Global Atmospheric Effects, U. Schumann, Ed., Lecture Notes in Engineering, Springer-Verlag, 138–153.

    • Crossref
    • Export Citation
  • Schumann, U., and K. Graf, 2013: Aviation-induced cirrus and radiation changes at diurnal timescales. J. Geophys. Res. Atmos., 118, 24042421, doi:10.1002/jgrd.50184.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., J. Ström, R. Busen, R. Baumann, K. Gierens, M. Krautstrunk, F. P. Schröder, and J. Stingl, 1996: In situ observations of particles in jet aircraft exhausts and contrails for different sulfur-containing fuels. J. Geophys. Res., 101, 68536870, doi:10.1029/95JD03405.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., H. Schlager, F. Arnold, R. Baumann, P. Haschberger, and O. Klemm, 1998: Dilution of aircraft exhaust plumes at cruise altitudes. Atmos. Environ., 32, 30973103, doi:10.1016/S1352-2310(97)00455-X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., R. Busen, and M. Plohr, 2000: Experimental test of the influence of propulsion efficiency on contrail formation. J. Aircr., 37, 10831087, doi:10.2514/2.2715.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., and et al. , 2002: Influence of fuel sulfur on the composition of aircraft exhaust plumes: The experiments SULFUR 1-7. J. Geophys. Res., 107, 4247, doi:10.1029/2001JD000813.

    • Search Google Scholar
    • Export Citation
  • Schumann, U., B. Mayer, K. Gierens, S. Unterstrasser, P. Jessberger, A. Petzold, C. Voigt, and J.-F. Gayet, 2011: Effective radius of ice particles in cirrus and contrails. J. Atmos. Sci., 68, 300321, doi:10.1175/2010JAS3562.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., K. Graf, H. Mannstein, and B. Mayer, 2012a: Contrails: Visible aviation induced climate impact. Atmospheric Physics: Background—Methods—Trends, U. Schumann, Ed., Research Topics in Aerospace Series, Vol. 1, Springer, 239–257, doi:10.1007/978-3-642-30183-4_15.

    • Crossref
    • Export Citation
  • Schumann, U., B. Mayer, K. Graf, and H. Mannstein, 2012b: A parametric radiative forcing model for contrail cirrus. J. Appl. Meteor. Climatol., 51, 13911406, doi:10.1175/JAMC-D-11-0242.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., R. Hempel, H. Flentje, M. Garhammer, K. Graf, S. Kox, H. Lösslein, and B. Mayer, 2013a: Contrail study with ground-based cameras. Atmos. Meas. Tech., 6, 35973612, doi:10.5194/amt-6-3597-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., P. Jeßberger, and C. Voigt, 2013b: Contrail ice particles in aircraft wakes and their climatic importance. Geophys. Res. Lett., 40, 28672872, doi:10.1002/grl.50539.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., J. E. Penner, Y. Chen, C. Zhou, and K. Graf, 2015: Dehydration effects from contrails in a coupled contrail-climate model. Atmos. Chem. Phys., 15, 11 17911 199, doi:10.5194/acp-15-11179-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., and et al. , 2017: Properties of individual contrails: A compilation of observations and some comparisons. Atmos. Chem. Phys., 17, 403438, doi:10.5194/acp-17-403-2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scorer, R. S., and L. J. Davenport, 1970: Contrails and aircraft downwash. J. Fluid Mech., 43, 451464, doi:10.1017/S0022112070002501.

  • Sharman, R. D., S. B. Trier, T. P. Lane, and J. D. Doyle, 2012: Sources and dynamics of turbulence in the upper troposphere and lower stratosphere: A review. Geophys. Res. Lett., 39, L12803, doi:10.1029/2012GL051996.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smit, H. G. J., S. Rohs, P. Neis, D. Boulanger, M. Krämer, A. Wahner, and A. Petzold, 2014: Reanalysis of upper troposphere humidity data from the MOZAIC programme for the period 1994 to 2009. Atmos. Chem. Phys., 14, 13 24113 255, doi:10.5194/acp-14-13241-2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Spichtinger, P., and M. Leschner, 2016: Horizontal scales of ice-supersaturated regions. Tellus, 68B, 29020, doi:10.3402/tellusb.v68.29020.

    • Search Google Scholar
    • Export Citation
  • Spichtinger, P., K. Gierens, and A. Dörnbrack, 2005: Formation of ice supersaturation by mesoscale gravity waves. Atmos. Chem. Phys., 5, 12431255, doi:10.5194/acp-5-1243-2005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Spinhirne, J. D., W. D. Hart, and D. P. Duda, 1998: Evolution of the morphology and microphysics of contrail cirrus from airborne remote sensing. Geophys. Res. Lett., 25, 11531156, doi:10.1029/97GL03477.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stettler, M. E. J., A. M. Boies, A. Petzold, and S. R. H. Barrett, 2013: Global civil aviation black carbon emissions. Environ. Sci. Technol., 47, 10 39710 404, doi:10.1021/es401356v.

    • Search Google Scholar
    • Export Citation
  • Stordal, F., G. Myhre, E. J. G. Stordal, W. B. Rossow, D. S. Lee, W. Arlander, and T. Svendby, 2005: Is there a trend in cirrus cloud cover due to aircraft traffic? Atmos. Chem. Phys., 5, 21552162, doi:10.5194/acp-5-2155-2005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ström, J., and S. Ohlsson, 1998: In situ measurements of enhanced crystal number densities in cirrus clouds caused by aircraft exhaust. J. Geophys. Res., 103, 11 35511 362, doi:10.1029/98JD00807.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stuber, N., M. Ponater, and R. Sausen, 2005: Why radiative forcing might fail as a predictor of climate change. Climate Dyn., 24, 497–510, doi:10.1007/s00382-004-0497-7.

    • Crossref
    • Export Citation
  • Sussmann, R., 1997: Optical properties of contrail-induced cirrus: Discussion of unusual halo phenomena. Appl. Opt., 36, 41954201, doi:10.1364/AO.36.004195.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sussmann, R., and K. Gierens, 1999: Lidar and numerical studies on the different evolution of vortex pair and secondary wake in young contrails. J. Geophys. Res., 104, 21312142, doi:10.1029/1998JD200034.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sussmann, R., and K. Gierens, 2001: Differences in early contrail evolution of two-engine versus four-engine aircraft: Lidar measurements and numerical simulations. J. Geophys. Res., 106, 48994911, doi:10.1029/2000JD900533.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thuman, W. C., and E. Robinson, 1954: Studies of Alaskan ice-fog particles. J. Meteor., 11, 151156, doi:10.1175/1520-0469(1954)011<0151:SOAIFP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Timko, M. T., and et al. , 2010: Gas turbine engine emissions—Part II: Chemical properties of particulate matter. J. Eng. Gas Turbines Power, 132, 061505, doi:10.1115/1.4000132.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tompkins, A., K. Gierens, and G. Rädel, 2007: Ice supersaturation in the ECMWF Integrated Forecast System. Quart. J. Roy. Meteor. Soc., 133, 5363, doi:10.1002/qj.14.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Unterstrasser, S., 2016: Properties of young contrails—A parametrisation based on large-eddy simulations. Atmos. Chem. Phys., 16, 20592082, doi:10.5194/acp-16-2059-2016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Unterstrasser, S., and K. Gierens, 2010a: Numerical simulations of contrail-to-cirrus transition—Part 1: An extensive parametric study. Atmos. Chem. Phys., 10, 20172036, doi:10.5194/acp-10-2017-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Unterstrasser, S., and K. Gierens, 2010b: Numerical simulations of contrail-to-cirrus transition—Part 2: Impact of initial ice crystal number, radiation, stratification, secondary nucleation and layer depth. Atmos. Chem. Phys., 10, 20372051, doi:10.5194/acp-10-2037-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Unterstrasser, S., and I. Sölch, 2012: Numerical modeling of contrail cluster formation. Proc. Third Int. Conf. on Transport, Atmosphere and Climate (TAC-3), Prien am Chiemsee, Germany, DLR, 114119.

  • Unterstrasser, S., and N. Görsch, 2014: Aircraft-type dependency of contrail evolution. J. Geophys. Res. Atmos., 119, 14 01514 027, doi:10.1002/2014JD022642.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Unterstrasser, S., I. Sölch, and K. Gierens, 2012: Cloud resolving modeling of contrail evolution. Atmospheric Physics: Background—Methods—Trends, U. Schumann, Ed., Research Topics in Aerospace Series, Vol. 1, Springer, 543–559, doi:10.1007/978-3-642-30183-4_33.

    • Crossref
    • Export Citation
  • Vázquez-Navarro, M., H. Mannstein, and S. Kox, 2015: Contrail life cycle and properties from 1 year of MSG/SEVIRI rapid-scan images. Atmos. Chem. Phys., 15, 87398749, doi:10.5194/acp-15-8739-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Voigt, C., and et al. , 2010: In-situ observations of young contrails—Overview and selected results from the CONCERT campaign. Atmos. Chem. Phys., 10, 90399056, doi:10.5194/acp-10-9039-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Voigt, C., and et al. , 2011: Extinction and optical depth of contrails. Geophys. Res. Lett., 38, L11806, doi:10.1029/2011GL047189.

  • Voigt, C., and et al. , 2016: ML-CIRRUS—The airborne experiment on natural cirrus and contrail cirrus with the high-altitude long-range research aircraft HALO. Bull. Amer. Meteor. Soc., doi:10.1175/BAMS-D-15-00213.1.

    • Crossref
    • Export Citation
  • Weickmann, H., 1945: Formen und Bildung atmosphärischer Eiskristalle. Beitr. Phys Atmos., 28, 12–52.

  • Wong, H.-W., and R. C. Miake-Lye, 2010: Parametric studies of contrail ice particle formation in jet regime using microphysical parcel modeling. Atmos. Chem. Phys., 10, 32613272, doi:10.5194/acp-10-3261-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wu, Y., and O. Pauluis, 2015: What is the representation of the moisture–tropopause relationship in CMIP5 models? J. Climate, 28, 48774889, doi:10.1175/JCLI-D-14-00543.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xie, Y., P. Yang, K.-N. Liou, P. Minnis, and D. P. Duda, 2012: Parameterization of contrail radiative properties for climate studies. Geophys. Res. Lett., 39, L00F02, doi:10.1029/2012GL054043.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, P., K. N. Liou, L. Bi, C. Liu, B. Q. Yi, and B. A. Baum, 2015: On the radiative properties of ice clouds: Light scattering, remote sensing, and radiation parameterization. Adv. Atmos. Sci., 32, 3263, doi:10.1007/s00376-014-0011-z.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhou, C., and J. E. Penner, 2014: Aircraft soot indirect effect on large-scale cirrus clouds: Is the indirect forcing by aircraft soot positive or negative? J. Geophys. Res. Atmos., 119, 11 30311 320, doi:10.1002/2014JD021914.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 448 448 110
PDF Downloads 364 364 94

On the Life Cycle of Individual Contrails and Contrail Cirrus

View More View Less
  • 1 Deutsches Zentrum für Luft- und Raumfahrt, Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany
  • | 2 National Center for Atmospheric Research, Boulder, Colorado
© Get Permissions
Full access

Abstract

The life cycle of individual (initially line shaped) contrails behind aircraft and of contrail cirrus (aged contrails mixed with other ice clouds) is described. The full contrail life cycle is covered, from ice formation for given water, heat, and particulate emissions; to changes in the jet, wake, and dispersion phases; through final sublimation or sedimentation. Contrail properties are deduced from various in situ, remote sensing, and model studies. Aerodynamically induced contrails and distrails are explained briefly. Contrails form both in clear air and inside cirrus. Young contrails consume most of the ambient ice supersaturation. Optical properties of contrails are age and humidity dependent. Contrail occurrence and radiative forcing depends on the ambient Earth–atmosphere conditions. Contrail cirrus seems to be optically thicker than assessed previously and may not only increase cirrus coverage but also thicken existing cirrus. Some observational constraints for contrail cirrus occurrence and radiative forcing are derived. Key parameters controlling contrail properties—besides aircraft and fuel properties, ambient pressure, temperature, and humidity—are the number of ice particles per flight distance surviving the wake vortex phase, the contrail depth, and particle sedimentation, wind shear, turbulence, and vertical motions controlling contrail dispersion. The climate impact of contrails depends among other things on the ratio of shortwave to longwave radiative forcing (RF) and on the efficacy with which contrail RF contributes to surface warming. Several open issues are identified, including renucleation from residuals of sublimated contrail ice particles.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Ulrich Schumann, ulrich.schumann@dlr.de

Abstract

The life cycle of individual (initially line shaped) contrails behind aircraft and of contrail cirrus (aged contrails mixed with other ice clouds) is described. The full contrail life cycle is covered, from ice formation for given water, heat, and particulate emissions; to changes in the jet, wake, and dispersion phases; through final sublimation or sedimentation. Contrail properties are deduced from various in situ, remote sensing, and model studies. Aerodynamically induced contrails and distrails are explained briefly. Contrails form both in clear air and inside cirrus. Young contrails consume most of the ambient ice supersaturation. Optical properties of contrails are age and humidity dependent. Contrail occurrence and radiative forcing depends on the ambient Earth–atmosphere conditions. Contrail cirrus seems to be optically thicker than assessed previously and may not only increase cirrus coverage but also thicken existing cirrus. Some observational constraints for contrail cirrus occurrence and radiative forcing are derived. Key parameters controlling contrail properties—besides aircraft and fuel properties, ambient pressure, temperature, and humidity—are the number of ice particles per flight distance surviving the wake vortex phase, the contrail depth, and particle sedimentation, wind shear, turbulence, and vertical motions controlling contrail dispersion. The climate impact of contrails depends among other things on the ratio of shortwave to longwave radiative forcing (RF) and on the efficacy with which contrail RF contributes to surface warming. Several open issues are identified, including renucleation from residuals of sublimated contrail ice particles.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Ulrich Schumann, ulrich.schumann@dlr.de

1. Introduction

Contrails (condensation trails) form behind aircraft as line-shaped cirrus clouds, with high concentrations of small ice particles compared to other cirrus (see Fig. 3-1). Contrails may form as “exhaust contrails” from water and particles emitted by the aircraft engines (Schumann 1996) or as “aerodynamic contrails” forming because of adiabatic cooling near curved surfaces of the aircraft (Gierens et al. 2009; Kärcher et al. 2009). Distrails (dissipation trails) and aircraft-induced cloud holes may also form (Heymsfield et al. 2011). Contrails are mostly short-lived but may persist for many hours when forming in ice-supersaturated air (Minnis et al. 1998). Individual contrails deform with time, often merge with other contrails and cirrus, and eventually form “contrail cirrus” (Schumann 2002). Contrail cirrus can be distinguished from other cirrus only when traced back to the formation process (Graf et al. 2012). Early studies discussed the visibility and detection aspects of contrails (aufm Kampe 1943; Brewer 1946; Appleman 1953; Ryan et al. 2011), and these studies contributed to the detection of ice supersaturation, contrail persistence, the dryness of the stratosphere, the Brewer–Dobson circulation (Brewer 2000), and hollow ice particles (Weickmann 1945). The climate impact got more attention later (Penner et al. 1999). The mean radiative forcing (RF) from contrails is likely positive, possibly contributing to global warming (Boucher et al. 2013). In contrast to many other climate effects discussed for aviation, contrail cirrus is observable (see Fig. 3-1f). This review summarizes the present understanding of contrail cirrus and identifies some open questions. The insight gained may be of relevance for cirrus research, contrail climate assessment, and mitigation (including optimized aircraft and engines, changed routing, and alternative fuels), not discussed here (Fuglestvedt et al. 2010; Lee et al. 2010; Grewe et al. 2014a; Brasseur et al. 2016). The paper describes first the formation and properties of “individual contrails.” This term is used instead of “line-shaped contrails” because it is not clear when a line-shaped contrail ends. The second part describes contrail cirrus.

Fig. 3-1.
Fig. 3-1.

Contrail types. (a) Exhaust contrail (photo by Josef P. Williams; Unterstrasser et al. 2012). (b) Aerodynamic contrail (photo by Dieter Klatt; Gierens et al. 2011). (c) Aircraft-induced lines and holes in supercooled liquid clouds (cloud-top temperatures −35° to −25°C); section of image with blue border lines, near northwest corner of Texas (29 Jan 2007, NASA, Jeff Schmaltz, MODIS Rapid Response Team). (d) Contrail visible shortly behind B747-400 engines, 38 000 ft, −61°C, 28 May 2004; photo by Robert Falk. (e) “Soot cirrus” observed at DLR, Oberpfaffenhofen, 0905 UTC 3 Nov 2013. (f) Persistent contrails west of lake Ammersee, Germany, photo by C. Koenig, DLR, 23 Jun 2002. (g) Persistent contrails and contrail cirrus, a false-color NOAA-12 AVHRR image, 5 Apr 1995, processed by DLR.

Citation: Meteorological Monographs 58, 1; 10.1175/AMSMONOGRAPHS-D-16-0005.1

2. Individual contrails

a. Mean contrail properties

Since contrails start as line-shaped clouds, unlike most other cirrus clouds, special integral properties are used. Just as other cirrus particles, each contrail particle has an individual mass mi, projected particle cross-section area Ai, habit, and orientation (see the appendix for a list of symbols). These properties plus the phase, composition, temperature, and wavelength determine the optical extinction efficiency Qext,i and other microphysical and optical properties of each particle (Hansen and Travis 1974). Integral properties peculiar to contrails are the geometrical cross-section area Ac, and the total crystal number Nice, total extinction EA, and total ice mass I per flight distance:
e3.1
e3.2
e3.3

Here, the local and the volume-mean ice particle concentrations ni and nice, extinction ε, and ice water content IWC occur, with mean extinction efficiency Qext and ice-bulk density ρice, besides optical depth τ and contrail width W. The summation sums over all ice particles in the contrail cross section. The above equations also define the volume and area-mean radius of the contrail particles, rvol and rarea. By tradition, the definitions are set up so they equal the geometrical radius in the idealized case of monodisperse spherical particles (Hansen and Travis 1974). The effective radius reff is defined by the ratio of mean particle volume to cross-section area, reff = 3IQext/(4ρiceEA). Again the factor (¾) enters for consistency with a hypothetical sphere radius. By definition, rvol/reff = . The ratio C = rvol/reff depends on ice particles sizes and habits and needs to be determined empirically; C ≤ 1 if the ice particles were spherical. Measured data collected for contrails show that C ≈ 0.7 ± 0.3 varies during the lifetime of the contrails and depends on ambient humidity (Schumann et al. 2011).

The aircraft wake evolution is traditionally divided into the jet, vortex, and dispersion regimes (Hoshizaki et al. 1975). After a roll-up phase (Misaka et al. 2015) overlapping with the jet regime, the vortex regime exhibits two phases: a first phase of a coherent counterrotating vortex pair and a second phase with rapid hydrodynamic vortex breakup and subsequent turbulent dissipation (Gerz and Holzäpfel 1999; Paoli and Shariff 2016).

b. Formation of exhaust contrails

1) Formation conditions

Exhaust contrails form during the jet phase because of engine emissions of water and particles [mainly soot, i.e., impure carbon particles resulting from incomplete combustion of hydrocarbon fuels (Bond et al. 2013; Petzold et al. 2013)] acting as cloud condensation nuclei (CCN). The emissions depend on fuel mass flow mF per flight distance (all-engine contribution) and on emission indices (EI) for exhaust species [gaseous or particulate (PEI); mass and number of emitted species per mass of fuel burned]. A fraction η = F/(QmF) of the specific combustion energy Q is used to propel the aircraft (depending on mF and thrust F), so that the fraction (1 − η) of Q appears in the young exhaust jet plume, partly in form of kinetic energy of the jets (Schumann 1996). The remainder heats the aircraft wake later, when all motions induced by the aircraft are dissipated. The term η is known as “overall propulsion efficiency” in engine technology (Penner et al. 1999). Contrails form when the exhaust gases exceed liquid saturation at least for a short time. Humidity (measured by partial vapor pressure) and heat (measured by temperature) in the exhaust plume decrease during mixing of the warm and humid exhaust gases with cool ambient air at about the same rate, along a straight mixing line in Fig. 3-2a. Relative humidity is the ratio of the partial pressure of water vapor in the exhaust relative to the saturation vapor pressure for given temperature. From the Clausius–Clapeyron equation, the saturation pressure follows a curve in this figure. Therefore, relative humidity is higher inside the plume than at engine exit and in ambient air. Maximum potential supersaturation is reached when the plume temperature reaches liquid maximum (LM) TLM. The plume humidity exceeds liquid saturation at least briefly when the ambient air temperature T is below a threshold temperature [liquid critical (LC)] TLC. Temperature TLC depends on ambient relative humidity RH (for liquid saturation) and a parameter G,
e3.4
with saturation pressure psat(T) over liquid water. From these equations, TLM(G) and TLC(G, RH) can be determined by Newton iteration or from approximate solutions (Schumann 2012). The parameter G covers the dependency of the threshold on ambient pressure p, and EIH2O, Q, and η, defined above, and the specific heat capacity cp of air, and molar masses MH2O and Mair of water and air. This Schmidt–Appleman criterion (SAC; Schumann 1996) does not consider phase changes and the process of ice production. It assumes quick conversion of kinetic energy from the engine jet into internal energy and simultaneous mixing of heat and water vapor between the exhaust jet and cloud-free ambient air. Within the accuracy of temperature and humidity measurements, the SAC has been verified experimentally (Busen and Schumann 1995; Schumann et al. 1996; Jensen et al. 1998b; Schumann et al. 2000). The measurements confirmed earlier findings that ice saturation is insufficient for formation of visible contrails. Figures 3-2b–f show probabilities of contrail formation properties for the global air traffic of 2006 and meteorology from the European Centre for Medium-Range Weather Forecasts (ECMWF). The plots show the frequency of flight conditions (p, T, η, RHi), in relation to threshold conditions. Potentially, without phase changes, 90% of the contrails experience liquid supersaturation (RHLM − 1) higher than 5% (up to 230% for low T), mainly near plume temperatures of 230 K for ambient temperatures near 220 K.
Fig. 3-2.
Fig. 3-2.

(a) Contrail formation principle (for G = 1.65 Pa K−1), identifying the points of maximum liquid saturation (LM), first liquid saturation (L1), and last liquid saturation (L2) for given environment (E, TE = 220 K, RHi = 1.1) and SAC threshold conditions (LC). Probability density functions of persistent contrail formation thermodynamics for 2006 air traffic from the FAA’s Aviation Climate Change Research Initiative (ACCRI) project and NWP data from ECMWF: (b) overall propulsion efficiency η; (c) pressure; (d) threshold temperature difference above ambience; (e) relative humidity RHi over ice and potential RHLM over liquid saturation at LM without phase changes; (f) temperature at L1, LM, L2, and E [colors as in (a)].

Citation: Meteorological Monographs 58, 1; 10.1175/AMSMONOGRAPHS-D-16-0005.1

2) Contrail ice formation

For conventional jet fuels and engines, contrail ice particles are frozen water droplets containing some soot or other CCN material (Kärcher et al. 1996; Wong and Miake-Lye 2010). Because of potentially high liquid supersaturation, liquid droplets form even on less hygroscopic CCN in the young contrail (Koehler et al. 2009). This is supported by particle refractive index measurements in young contrails suggesting internal mixtures of soot in contrail ice particles (Kuhn et al. 1998). A significant reduction of interstitial nonvolatile particles has been observed when contrails form, indicating that exhaust soot indeed participates in ice formation (Schröder et al. 1998). Besides soot, volatile aerosol forming in the engine exhaust plume may also contribute to ice nucleation, in particular for low soot particle emissions (<1014 kg−1) and low ambient temperatures (<213 K; Kärcher and Yu 2009; Wong and Miake-Lye 2010). High concentrations of volatile aerosol have been observed (Fahey et al. 1995). The effect of fuel sulfur content is smaller than expected initially (Schumann et al. 1996; Jurkat et al. 2011).

For ~10% of all contrails, the ambient temperature is only 1 K below the threshold temperature. Here, details of the CCN become important (Kärcher et al. 2015). Ice particles form either by homogeneous freezing of the liquid droplets (not involving ice nuclei) or heterogeneously by ice nuclei (Wong and Miake-Lye 2010). The fraction fc of soot particles forming droplets decreases with soot loading because of the increased competition for the vapor available for condensation (Kärcher et al. 1996; Paoli et al. 2013). For alternative fuels, with different aerosol and aerosol precursor emissions, ice may form by freezing of water droplets forming on soot (possibly heterogeneously) for high soot concentrations and from volatile material (homogeneously) for less soot (Rojo et al. 2015).

The number Nice of ice particles per flight distance forming in the young contrail depends also on the time available for condensation and for ice formation. Without freezing, the contrail particles would soon evaporate even in ice-supersaturated but liquid-subsaturated air. The liquid droplets freeze quickly after formation because of low temperature and high relative humidity in the contrail. Liquid saturation may persist more than 10 s along the plume axis but <0.1 s at the outer edge of the exhaust plume. Faint contrails become visible to passengers already close to the engine exit for low temperature (see Fig. 3-1d) and about a wing span after engines under threshold conditions (Busen and Schumann 1995). In the interior of the well-mixed plume, condensation starts many wing spans behind the engine (Schumann et al. 1996; Paoli and Shariff 2016). Outside the plume center, mixing proceeds far quicker, leaving less time for condensing water during liquid supersaturation. Ice particles at the outer edge of contrails experience higher relative humidity and less competition for the available moisture than in the center, thereby getting larger than in the contrail interior, as observed (Petzold et al. 1997; Heymsfield et al. 1998).

3) Mixing and plume dilution

Mixing of the exhaust jet plume depends on interaction between the jet and the wake vortices in the roll-up phase (Khou et al. 2015), with similar characteristic time scales of mixing and condensation (Wong and Miake-Lye 2010; Paoli et al. 2013). The wide range of time scales may be important for contrail formation from alternative fuels.

Mixing can be expressed in terms of a dilution ratio Ndil (Schumann et al. 1998). Here, Ndil is the mass of air inside the plume per mass of fuel burned, both per flight distance. This definition avoids any dependence on air–fuel ratio in the engine that arises if dilution is defined relative to engine exhaust mass flow. Measurements have shown that the dilution of tracers near the plume center follows approximately
e3.5
where t0 = 1 s. This result is a bit surprising because it is independent of aircraft and atmosphere scales, but has been confirmed by various measurements and applied successfully for estimates of aircraft exhaust concentrations and plume ages (Schäuble et al. 2009; Rojo et al. 2015).

4) Soot emissions

Since other emissions scale with fuel consumption mF per flight distance and with an emission index, it makes sense to define an apparent particle emission index PEIice such that Nice = PEIicemF. If each ice particle would share the same amount of exhaust water, in ice-saturated ambient air, and after cooling to ambient temperature, then the volume-mean radius would be
e3.6
implying rvol ≈ 0.67 μm for EIH2O = 1.24 and PEIice = 1015 kg−1, with ρice ≈ 917 kg m−3 as ice-bulk density (if without air bubbles). This simple analysis shows the high importance of PEIice for contrail properties. Since we expect PEIice = fcPEIsoot, we need to know fc and the soot number emission index.

Soot formation, mainly from fuel aromatics, is fuel, engine, and power dependent (Moore et al. 2015). Lower fuel aromatics (naphthalene) content reduces PEIsoot (Braun-Unkhoff and Riedel 2015). Modern engines tend to emit less soot than older ones (Lee et al. 2010). The mass of soot particles msoot, relating EIsoot = msootPEIsoot, increases with thrust setting (Timko et al. 2010). The mass-specific soot emission index EIsoot is traditionally determined from ground tests (using smoke number measurements), and more recently from ground-based direct measurements (Timko et al. 2010; Boies et al. 2015). EIsoot at cruise can be estimated from ground-based measurements and engine parameters (Peck et al. 2013). Stettler et al. (2013) show that current methods deriving aircraft soot mass emissions from smoke number data may underestimate the mass emissions by about a factor of 3, partly because smaller particles contribute little to the smoke number measurement. From the few experimental data points from in situ measurements behind cruising civil subsonic aircraft, in particular during the former Subsonic Aircraft Contrail and Cloud Effects Special Study (SUCCESS; Anderson et al. 1998) and SULFUR projects (Petzold et al. 1999; Schumann et al. 2002), one finds PEIsoot of 0.2 to 10 × 1015 kg−1 and msoot ≈ (4 ± 2) × 10−20 kg. More information is required on soot number emissions (PEIsoot) and on the fraction fc of soot acting as CCN for given contrail formation conditions.

5) Number of ice particles formed

Ice particles and soot particles under cruise conditions are difficult to measure simultaneously. Part of the soot gets scavenged by contrail ice (Schröder et al. 1998), and therefore ice and soot are measured behind aircraft separately in dry or wet plumes (Brock et al. 2000). The SULFUR project showed that the number of ice particles in young contrails is comparable to the number of soot particles emitted from the engines. PEIice increases slightly (by a factor of <2) when fuel sulfur content increases from 6 to 2800 μg g−1. The effective PEIice derived from in situ contrail ice particle measurements (Schröder et al. 2000) with dilution from Eq. (5) varies between 1014 and 1015 kg−1 (Schumann 2005). During a more recent field experiment, the Contrail and Cirrus Experiment (CONCERT; Voigt et al. 2010), ice particle concentrations were measured in contrails behind various airliners for contrails of a few minutes’ age. The derived PEIice values vary between 0.7 and 7.2 × 1014 kg−1, with the higher values in the secondary wake above the sinking primary wake (Jeßberger et al. 2013). The results were compared with PEIsoot values derived from ground measurements for given flight conditions, and it was found that PEIice is larger than the PEIsoot (Schumann et al. 2013b). This suggests that aircraft either emit more soot particles suitable for contrail formation than estimated or that particle losses are less than predicted. The effect of alternative fuels on particle emissions and the formation of contrails has been investigated since May 2014 within the Alternative-Fuel Effects on Contrails and Cruise Emissions (ACCESS II) and Emission and Climate Impact of Alternative Fuels Experiment (ECLIF) projects (B. Anderson and H. Schlager, American Geophysical Union, 2015, personal communication). In summary, Nice,0 in the young contrail can be estimated from the soot emissions and the fuel consumption per unit flight distance,
e3.7

c. Aerodynamic contrails, distrails, and cloud holes

Aerodynamic contrails show nicely colored iridescent line clouds (Fig. 3-1b). Contrail iridescence was observed for contrails early (Sassen 1979). Aerodynamic contrails form from intense adiabatic cooling in the airflow over aircraft wings (Gierens et al. 2009). The colors in the aerodynamic contrail are explained by the rapid growth of nearly monodisperse particles, which are visible when observed close to the sun (Kärcher et al. 2009). Only recently it was shown that most of the visible particles form from homogeneous droplet nucleation (Jansen and Heymsfield 2015). The meteorological conditions for aerodynamic contrail formation have been examined in a case study and globally (Gierens et al. 2011; Gierens and Dilger 2013). Visible aerodynamic contrails occur in an altitude range between roughly 540 and 250 hPa, preferentially at temperatures between −20° and −50°C, and for RH > 80% (Jansen and Heymsfield 2015). The number of ice particles formed in aerodynamic contrails is not well known, but likely smaller than for exhaust contrails (Kärcher et al. 2009). Often exhaust and aerodynamic contrails form simultaneously (see Figs. 3-1a,b). Aerodynamically induced ice particles may cause inadvertent seeding of ice in supercooled clouds. This explains observed aircraft-induced holes in clouds at temperatures between −10° and −20°C (see Fig. 3-1c). These holes may contribute to snow precipitation near airports (Heymsfield et al. 2011). Distrails (dissipation trails) are visible occasionally from ground and in satellite images as linear gaps in clouds (Duda and Minnis 2002). Distrails may result from exhaust or from mixing induced by aircraft (Scorer and Davenport 1970). For nice distrail photos and historical remarks, see Pedgley (2008).

d. Contrail wake vortex phase

Wake vortices depend on aircraft properties including aircraft wing span s, mass M, and true airspeed V, and on atmosphere parameters, such as air density ρ, Brunt–Väisälä frequency NBV, turbulence dissipation rate εt, and gravity g, which together define wake vortex scales:
e3.8

Here, b0 measure the lateral distance between the vortex lines, Γ the integral vortex circulation; and t0, w0, , and are the related time, velocity, stratification, and dissipation scales, respectively. The wake vortex forms because of aerodynamics: Lift balances aircraft weight by inducing downward momentum on the air behind the aircraft wing. Lift requires circulation (Kutta–Joukowski theorem). Circulation is the integral of velocity along a line around the wing and equals the integral of the open surface bounded by that line (Stokes theorem). Vorticity departs with the flow from the wing rear edges or the wing tips depending on the lift distribution along the wing (Anderson 2010). Some distance behind the aircraft, a vortex pair forms, which sinks with mean speed w0 initially, until buoyancy becomes important or until hydrodynamic instabilities have grown sufficiently to cause a sudden breakup into dissipating turbulence. The jet regime ends ~4–40 wing spans behind the aircraft, depending on speed, engine number, and engine positions, when the exhaust jets and the freshly formed contrails got captured in the wake vortex system (Gerz and Ehret 1996). Depending on this interaction, most of the exhaust gets captured in the primary wake vortex (Greene 1986). Part of the exhaust stays outside and above the sinking primary wake and forms the “secondary wake” (Misaka et al. 2012; Holzäpfel 2014; Paoli and Shariff 2016).

Only a fraction fs of the ice crystals formed in the jet survives the transition from contrail formation until final decay of the wake vortices (Sussmann and Gierens 1999). Any initial ice supersaturation in the contrail gets reduced rapidly by deposition of the vapor excess on the many ice particles in the jets, before the vortex has descended much and reached its lowest altitude. The sinking vortex experiences adiabatic heating (Greene 1986), which causes a slight local subsaturation around the ice particles, even sensitive to the Kelvin effect, that is, a reduction of saturation pressure depending on particle curvature and surface tension (Naiman et al. 2011; Lewellen 2012). As a consequence, the smaller ice particles sublimate and the number of ice particles decreases (Lewellen and Lewellen 2001). The secondary wake contains fewer but larger ice particles and binds more ice water because of quicker mixing with ambient humid air and less heating by adiabatic sinking. At low ambient humidity, the primary wake may sublimate after some time while the secondary wake persists longer (Sussmann and Gierens 2001). The fraction fs of ice particles surviving the wake vortex depends on temperature and humidity, and on the wake vortex scales, and also on the number and size of ice particles formed in the jet phase. The fraction can be estimated from a parameterization based on several recent large-eddy simulation (LES) studies (Unterstrasser 2016). As a consequence, any decrease in particle emissions causes a less than linear decrease in the number of ice particles. It would be important to validate these model results by measurements.

A set of data of individual contrails for ages from seconds to hours is compiled in Fig. 3-3 from previous in situ and remote sensing observations and from a recent model study. The data include ice particle concentrations, sizes, ice water content, geometrical depth, width, and optical depth. Integral properties (Ac, Nice, EA, I) are also available (Schumann et al. 2017). The observations support the assumption that the number of ice particles in contrails is controlled by the heat, humidity, and aerosol in the engine exhaust and the formation process in the jet phase, and they decrease thereafter. Artifacts produced by crystal shattering on the inlets of the particle probes can yield measurement errors, in particular when large particles are present (Korolev et al. 2011). Most contrail particles, formed at low ambient temperature, are small and, hence, shattering is likely small (Febvre et al. 2009; Voigt et al. 2011). The data synthesis shows no obvious indication, like exceptionally high ice particle concentrations, that ice particle shattering at instrument inlets had strong effects on past contrail measurements.