Interactions between Gravity Waves and Cirrus Clouds: Asymptotic Modeling of Wave-Induced Ice Nucleation

Stamen I. Dolaptchiev aInstitut für Atmosphäre und Umwelt, Goethe-Universität Frankfurt, Frankfurt, Germany

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Peter Spichtinger bJohannes Gutenberg-Universität Mainz, Mainz, Germany

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Manuel Baumgartner bJohannes Gutenberg-Universität Mainz, Mainz, Germany

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Ulrich Achatz aInstitut für Atmosphäre und Umwelt, Goethe-Universität Frankfurt, Frankfurt, Germany

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Abstract

We present an asymptotic approach for the systematic investigation of the effect of gravity waves (GWs) on ice clouds formed through homogeneous nucleation. In particular, we consider high- and midfrequency GWs in the tropopause region driving the formation of ice clouds, modeled with a double-moment bulk ice microphysics scheme. The asymptotic approach allows for identifying reduced equations for self-consistent description of the ice dynamics forced by GWs including the effects of diffusional growth and nucleation of ice crystals. Further, corresponding analytical solutions for a monochromatic GW are derived under a single-parcel approximation. The results provide a simple expression for the nucleated number of ice crystals in a nucleation event. It is demonstrated that the asymptotic solutions capture the dynamics of the full ice model and accurately predict the nucleated ice crystal number. The present approach is extended to allow for superposition of GWs, as well as for variable ice crystal mean mass in the deposition. Implications of the results for an improved representation of GW variability in cirrus parameterizations are discussed.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

This article is included in the Multi-Scale Dynamics of Gravity Waves (MS-GWaves) Special Collection.

Corresponding author: Stamen Dolaptchiev, dolaptchiev@iau.uni-frankfurt.de

Abstract

We present an asymptotic approach for the systematic investigation of the effect of gravity waves (GWs) on ice clouds formed through homogeneous nucleation. In particular, we consider high- and midfrequency GWs in the tropopause region driving the formation of ice clouds, modeled with a double-moment bulk ice microphysics scheme. The asymptotic approach allows for identifying reduced equations for self-consistent description of the ice dynamics forced by GWs including the effects of diffusional growth and nucleation of ice crystals. Further, corresponding analytical solutions for a monochromatic GW are derived under a single-parcel approximation. The results provide a simple expression for the nucleated number of ice crystals in a nucleation event. It is demonstrated that the asymptotic solutions capture the dynamics of the full ice model and accurately predict the nucleated ice crystal number. The present approach is extended to allow for superposition of GWs, as well as for variable ice crystal mean mass in the deposition. Implications of the results for an improved representation of GW variability in cirrus parameterizations are discussed.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

This article is included in the Multi-Scale Dynamics of Gravity Waves (MS-GWaves) Special Collection.

Corresponding author: Stamen Dolaptchiev, dolaptchiev@iau.uni-frankfurt.de
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  • Achatz, U., 2022: Atmospheric Dynamics. Springer, 554 pp., https://doi.org/10.1007/978-3-662-63941-2.

  • Achatz, U., R. Klein, and F. Senf, 2010: Gravity waves, scale asymptotics and the pseudo-incompressible equations. J. Fluid Mech., 663, 120147, https://doi.org/10.1017/S0022112010003411.

    • Search Google Scholar
    • Export Citation
  • Achatz, U., B. Ribstein, F. Senf, and R. Klein, 2017: The interaction between synoptic-scale balanced flow and a finite-amplitude mesoscale wave field throughout all atmospheric layers: Weak and moderately strong stratification. Quart. J. Roy. Meteor. Soc., 143, 342361, https://doi.org/10.1002/qj.2926.

    • Search Google Scholar
    • Export Citation
  • Atlas, R., and C. S. Bretherton, 2023: Aircraft observations of gravity wave activity and turbulence in the tropical tropopause layer: Prevalence, influence on cirrus clouds, and comparison with global storm-resolving models. Atmos. Chem. Phys., 23, 40094030, https://doi.org/10.5194/acp-23-4009-2023.

    • Search Google Scholar
    • Export Citation
  • Baumgartner, M., and P. Spichtinger, 2019: Homogeneous nucleation from an asymptotic point of view. Theor. Comput. Fluid Dyn., 33, 83106, https://doi.org/10.1007/s00162-019-00484-0.

    • Search Google Scholar
    • Export Citation
  • Baumgartner, M., R. Weigel, A. H. Harvey, F. Plöger, U. Achatz, and P. Spichtinger, 2020: Reappraising the appropriate calculation of a common meteorological quantity: Potential temperature. Atmos. Chem. Phys., 20, 15 58515 616, https://doi.org/10.5194/acp-20-15585-2020.

    • Search Google Scholar
    • Export Citation
  • Baumgartner, M., C. Rolf, J.-U. Grooß, J. Schneider, T. Schorr, O. Möhler, P. Spichtinger, and M. Krämer, 2022: New investigations on homogeneous ice nucleation: The effects of water activity and water saturation formulations. Atmos. Chem. Phys., 22, 6591, https://doi.org/10.5194/acp-22-65-2022.

    • Search Google Scholar
    • Export Citation
  • Bölöni, G., B. Ribstein, J. Muraschko, C. Sgoff, J. Wei, and U. Achatz, 2016: The interaction between atmospheric gravity waves and large-scale flows: An efficient description beyond the nonacceleration paradigm. J. Atmos. Sci., 73, 48334852, https://doi.org/10.1175/JAS-D-16-0069.1.

    • Search Google Scholar
    • Export Citation
  • Bölöni, G., Y.-H. Kim, S. Borchert, and U. Achatz, 2021: Toward transient subgrid-scale gravity wave representation in atmospheric models. Part I: Propagation model including nondissipative wave–mean-flow interactions. J. Atmos. Sci., 78, 13171338, https://doi.org/10.1175/JAS-D-20-0065.1.

    • Search Google Scholar
    • Export Citation
  • Bramberger, M., and Coauthors, 2022: First super-pressure balloon-borne fine-vertical-scale profiles in the upper TTL: Impacts of atmospheric waves on cirrus clouds and the QBO. Geophys. Res. Lett., 49, e2021GL097596, https://doi.org/10.1029/2021GL097596.

    • Search Google Scholar
    • Export Citation
  • Corcos, M., A. Hertzog, R. Plougonven, and A. Podglajen, 2021: Observation of gravity waves at the tropical tropopause using superpressure balloons. J. Geophys. Res. Atmos., 126, e2021JD035165, https://doi.org/10.1029/2021JD035165.

    • Search Google Scholar
    • Export Citation
  • Corcos, M., A. Hertzog, R. Plougonven, and A. Podglajen, 2023: A simple model to assess the impact of gravity waves on ice-crystal populations in the tropical tropopause layer. Atmos. Chem. Phys., 23, 69236936, https://doi.org/10.5194/acp-23-6923-2023.

    • Search Google Scholar
    • Export Citation
  • Dean, S. M., J. Flowerdew, B. N. Lawrence, and S. D. Eckermann, 2007: Parameterisation of orographic cloud dynamics in a GCM. Climate Dyn., 28, 581597, https://doi.org/10.1007/s00382-006-0202-0.

    • Search Google Scholar
    • Export Citation
  • Dinh, T., A. Podglajen, A. Hertzog, B. Legras, and R. Plougonven, 2016: Effect of gravity wave temperature fluctuations on homogeneous ice nucleation in the tropical tropopause layer. Atmos. Chem. Phys., 16, 3546, https://doi.org/10.5194/acp-16-35-2016.

    • Search Google Scholar
    • Export Citation
  • Dolaptchiev, S. I., U. Achatz, and I. Timofeyev, 2013: Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation. Theor. Comput. Fluid Dyn., 27, 297317, https://doi.org/10.1007/s00162-012-0270-1.

    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 1989: Improving the anelastic approximation. J. Atmos. Sci., 46, 14531461, https://doi.org/10.1175/1520-0469(1989)046<1453:ITAA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gasparini, B., A. Meyer, D. Neubauer, S. Münch, and U. Lohmann, 2018: Cirrus cloud properties as seen by the CALIPSO satellite and ECHAM-HAM global climate model. J. Climate, 31, 19832003, https://doi.org/10.1175/JCLI-D-16-0608.1.

    • Search Google Scholar
    • Export Citation
  • Gierens, K., 2003: On the transition between heterogeneous and homogeneous freezing. Atmos. Chem. Phys., 3, 437446, https://doi.org/10.5194/acp-3-437-2003.

    • Search Google Scholar
    • Export Citation
  • Haag, W., and B. Kärcher, 2004: The impact of aerosols and gravity waves on cirrus clouds at midlatitudes. J. Geophys. Res., 109, D12202, https://doi.org/10.1029/2004JD004579.

    • Search Google Scholar
    • Export Citation
  • Hertzog, A., M. J. Alexander, and R. Plougonven, 2012: On the intermittency of gravity wave momentum flux in the stratosphere. J. Atmos. Sci., 69, 34333448, https://doi.org/10.1175/JAS-D-12-09.1.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., and L. M. Miloshevich, 1993: Homogeneous ice nucleation and supercooled liquid water in orographic wave clouds. J. Atmos. Sci., 50, 23352353, https://doi.org/10.1175/1520-0469(1993)050<2335:HINASL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Holmes, M. H., 2013: Introduction to Perturbation Methods. Texts in Applied Mathematics, Vol. 20, Springer, 438 pp.

  • Hoose, C., and O. Möhler, 2012: Heterogeneous ice nucleation on atmospheric aerosols: A review of results from laboratory experiments. Atmos. Chem. Phys., 12, 98179854, https://doi.org/10.5194/acp-12-9817-2012.

    • Search Google Scholar
    • Export Citation
  • Jensen, E., and L. Pfister, 2004: Transport and freeze-drying in the tropical tropopause layer. J. Geophys. Res., 109, D02207, https://doi.org/10.1029/2003JD004022.

    • Search Google Scholar
    • Export Citation
  • Joos, H., P. Spichtinger, U. Lohmann, J.-F. Gayet, and A. Minikin, 2008: Orographic cirrus in the global climate model ECHAM5. J. Geophys. Res., 113, D18205, https://doi.org/10.1029/2007JD009605.

    • Search Google Scholar
    • Export Citation
  • Joos, H., P. Spichtinger, and U. Lohmann, 2009: Orographic cirrus in a future climate. Atmos. Chem. Phys., 9, 78257845, https://doi.org/10.5194/acp-9-7825-2009.

    • Search Google Scholar
    • Export Citation
  • Kärcher, B., and U. Lohmann, 2002: A parameterization of cirrus cloud formation: Homogeneous freezing of supercooled aerosols. J. Geophys. Res., 107, 4010, https://doi.org/10.1029/2001JD000470.

    • Search Google Scholar
    • Export Citation
  • Kärcher, B., and J. Ström, 2003: The roles of dynamical variability and aerosols in cirrus cloud formation. Atmos. Chem. Phys., 3, 823838, https://doi.org/10.5194/acp-3-823-2003.

    • Search Google Scholar
    • Export Citation
  • Kärcher, B., and U. Burkhardt, 2008: A cirrus cloud scheme for general circulation models. Quart. J. Roy. Meteor. Soc., 134, 14391461, https://doi.org/10.1002/qj.301.

    • Search Google Scholar
    • Export Citation
  • Kärcher, B., and A. Podglajen, 2019: A stochastic representation of temperature fluctuations induced by mesoscale gravity waves. J. Geophys. Res. Atmos., 124, 11 50611 529, https://doi.org/10.1029/2019JD030680.

    • 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, https://doi.org/10.5194/acp-13-9021-2013.

    • Search Google Scholar
    • Export Citation
  • Kim, J.-E., and Coauthors, 2016: Ubiquitous influence of waves on tropical high cirrus cloud. Geophys. Res. Lett., 43, 58955901, https://doi.org/10.1002/2016GL069293.

    • Search Google Scholar
    • Export Citation
  • Kim, Y.-H., G. Bölöni, S. Borchert, H.-Y. Chun, and U. Achatz, 2021: Toward transient subgrid-scale gravity wave representation in atmospheric models. Part II: Wave intermittency simulated with convective sources. J. Atmos. Sci., 78, 13391357, https://doi.org/10.1175/JAS-D-20-0066.1.

    • Search Google Scholar
    • Export Citation
  • Koop, T., B. Luo, A. Tsias, and T. Peter, 2000: Water activity as the determinant for homogeneous ice nucleation in aqueous solutions. Nature, 406, 611614, https://doi.org/10.1038/35020537.

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

    • Search Google Scholar
    • Export Citation
  • Krämer, M., and Coauthors, 2009: Ice supersaturations and cirrus cloud crystal numbers. Atmos. Chem. Phys., 9, 35053522, https://doi.org/10.5194/acp-9-3505-2009.

    • Search Google Scholar
    • Export Citation
  • Krämer, M., and Coauthors, 2016: A microphysics guide to cirrus clouds—Part 1: Cirrus types. Atmos. Chem. Phys., 16, 34633483, https://doi.org/10.5194/acp-16-3463-2016.

    • Search Google Scholar
    • Export Citation
  • Krämer, M., and Coauthors, 2020: A microphysics guide to cirrus—Part 2: Climatologies of clouds and humidity from observations. Atmos. Chem. Phys., 20, 12 56912 608, https://doi.org/10.5194/acp-20-12569-2020.

    • Search Google Scholar
    • Export Citation
  • Podglajen, A., A. Hertzog, R. Plougonven, and B. Legras, 2016: Lagrangian temperature and vertical velocity fluctuations due to gravity waves in the lower stratosphere. Geophys. Res. Lett., 43, 35433553, https://doi.org/10.1002/2016GL068148.

    • Search Google Scholar
    • Export Citation
  • Podglajen, A., R. Plougonven, A. Hertzog, and E. Jensen, 2018: Impact of gravity waves on the motion and distribution of atmospheric ice particles. Atmos. Chem. Phys., 18, 10 79910 823, https://doi.org/10.5194/acp-18-10799-2018.

    • Search Google Scholar
    • Export Citation
  • Pruppacher, H. R., and J. D. Klett, 2010: Microphysics of Clouds and Precipitation. Springer, 954 pp., https://doi.org/10.1007/978-0-306-48100-0.

  • Ren, C., and A. R. Mackenzie, 2005: Cirrus parametrization and the role of ice nuclei. Quart. J. Roy. Meteor. Soc., 131, 15851605, https://doi.org/10.1256/qj.04.126.

    • Search Google Scholar
    • Export Citation
  • Spichtinger, P., and K. M. Gierens, 2009: Modelling of cirrus clouds—Part 1a: Model description and validation. Atmos. Chem. Phys., 9, 685706, https://doi.org/10.5194/acp-9-685-2009.

    • Search Google Scholar
    • Export Citation
  • Spichtinger, P., and D. J. Cziczo, 2010: Impact of heterogeneous ice nuclei on homogeneous freezing events. J. Geophys. Res., 115, D14208, https://doi.org/10.1029/2009JD012168.

    • Search Google Scholar
    • Export Citation
  • Spichtinger, P., and M. Krämer, 2013: Tropical tropopause ice clouds: A dynamic approach to the mystery of low crystal numbers. Atmos. Chem. Phys., 13, 98019818, https://doi.org/10.5194/acp-13-9801-2013.

    • Search Google Scholar
    • Export Citation
  • Spichtinger, P., P. Marschalik, and M. Baumgartner, 2023: Impact of formulations of the homogeneous nucleation rate on ice nucleation events in cirrus. Atmos. Chem. Phys., 23, 20352060, https://doi.org/10.5194/acp-23-2035-2023.

    • Search Google Scholar
    • Export Citation
  • Spreitzer, E. J., M. P. Marschalik, and P. Spichtinger, 2017: Subvisible cirrus clouds—A dynamical system approach. Nonlinear Processes Geophys., 24, 307328, https://doi.org/10.5194/npg-24-307-2017.

    • Search Google Scholar
    • Export Citation
  • Wang, M., and J. E. Penner, 2010: Cirrus clouds in a global climate model with a statistical cirrus cloud scheme. Atmos. Chem. Phys., 10, 54495474, https://doi.org/10.5194/acp-10-5449-2010.

    • Search Google Scholar
    • Export Citation
  • Zhang, Y., A. Macke, and F. Albers, 1999: Effect of crystal size spectrum and crystal shape on stratiform cirrus radiative forcing. Atmos. Res., 52, 5975, https://doi.org/10.1016/S0169-8095(99)00026-5.

    • Search Google Scholar
    • Export Citation
  • Zhou, C., J. E. Penner, G. Lin, X. Liu, and M. Wang, 2016: What controls the low ice number concentration in the upper troposphere? Atmos. Chem. Phys., 16, 12 41112 424, https://doi.org/10.5194/acp-16-12411-2016.

    • Search Google Scholar
    • Export Citation
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