• Alexander, M. J., 1996: A simulated spectrum of convectively generated gravity waves: Propagation from the tropopause to the mesopause and effects on the middle atmosphere. J. Geophys. Res.,101, 1571–1588.

  • ——, 1998: Interpretations of observed climatological patterns in stratospheric gravity wave variance. J. Geophys. Res.,103, 8627–8640.

  • ——, and L. Pfister, 1995: Gravity wave momentum flux in the lower stratosphere over convection. Geophys. Res. Lett.,22, 2029–2032.

  • ——, and K. H. Rosenlof, 1996: Nonstationary gravity wave forcing of the stratospheric zonal mean wind. J. Geophys. Res.,101, 23 465–23 474.

  • ——, and J. R. Holton, 1997: A model study of zonal forcing in the equatorial stratosphere by convectively induced gravity waves. J. Atmos. Sci.,54, 408–419.

  • Andreassen, O., C. E. Wasberg, D. C. Fritts, and J. R. Isler, 1994: Gravity wave breaking in two and three dimensions, 1. Model description and comparison of two-dimensional evolutions. J. Geophys. Res.,99, 8095–8108.

  • Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. Academic Press, 489 pp.

  • Bacmeister, J. T., 1993: Mountain-wave drag in the stratosphere and mesosphere inferred from observed winds and a simple mountain-wave parameterization scheme. J. Atmos. Sci.,50, 377–399.

  • Broutman, D., C. Macaskill, M. E. McIntyre, and J. W. Rottmann, 1997: On Doppler-spreading models of internal waves. Geophys. Res. Lett.,24, 2813–2816.

  • Chang, J. L., S. K. Avery, A. C. Riddle, S. E. Palo, and K. S. Gage, 1997: First results of tropospheric gravity wave momentum flux measurements over Christmas Island. Radio Sci.,32, 727–748.

  • Coy, L., and D. C. Fritts, 1988: Gravity wave heat fluxes: A Lagrangian approach. J. Atmos. Sci.,45, 1770–1780.

  • Dewan, E. M., and R. E. Good, 1986: Saturation and the “universal” spectrum for vertical profiles of horizontal scalar winds in the atmosphere. J. Geophys. Res.,91, 2742–2748.

  • ——, and Coauthors, 1998: MSX satellite observations of thunderstorm-generated gravity waves in mid-wave infrared images of the upper stratosphere. Geophys. Res. Lett.,25, 939–942.

  • Dunkerton, T. J., 1984: Inertia–gravity waves in the stratosphere. J. Atmos. Sci.,41, 3396–3404.

  • ——, 1989: Theory of internal gravity wave saturation. Pure Appl. Geophys.,130, 373–397.

  • ——, 1997: The role of gravity waves in the quasi-biennial oscillation. J. Geophys. Res.,102, 26 053–26 076.

  • Durran, D. D., 1995: Do breaking mountain waves decelerate the local mean flow? J. Atmos. Sci.,52, 4010–4032.

  • Eckermann, S. D., 1997: Influence of wave propagation on the Doppler spreading of atmospheric gravity waves. J. Atmos. Sci.,54, 2554–2573.

  • ——, and C. J. Marks, 1996: An idealized ray model of gravity wave-tidal interactions. J. Geophys. Res.,101, 21 195–21 212.

  • Fleming, E. L., S. Chandra, J. J. Barnett, and M. Corney, 1990: Zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude. Adv. Space Res.,10 (12), 11–59.

  • Fritts, D. C., 1984: Gravity wave saturation in the middle atmosphere:A review of theory and observations. Rev. Geophys. Space Phys.,22, 275–308.

  • ——, 1989: A review of gravity wave saturation processes, effects, and variability in the middle atmosphere. Pure Appl. Geophys.,130, 343–371.

  • ——, and T. J. Dunkerton, 1985: Fluxes of heat and constituents due to convectively unstable gravity waves. J. Atmos. Sci.,42, 549–556.

  • ——, and R. A. Vincent, 1987: Mesospheric momentum flux studies at Adelaide, Australia: Observations and a gravity wave–tidal interaction model. J. Atmos. Sci.,44, 605–619.

  • ——, and W. Lu, 1993: Spectral estimates of gravity wave energy and momentum fluxes. Part II: Parameterization of wave forcing and variability. J. Atmos. Sci.,50, 3695–3713.

  • ——, and T. E. VanZandt, 1993: Spectral estimates of gravity wave energy and momentum fluxes. Part I: Energy dissipation, acceleration, and constraints. J. Atmos. Sci.,50, 3685–3694.

  • ——, T. Tsuda, T. E. VanZandt, S. A. Smith, T. Sato, S. Fukao, and S. Kato, 1990: Studies of velocity fluctuations in the lower atmosphere using the MU radar. Part II: Momentum fluxes and energy densities. J. Atmos. Sci.,47, 51–66.

  • ——, J. R. Isler, and Ø. Andreassen, 1994: Gravity wave breaking in two and three dimensions, 2: Three-dimensional evolution and instability structure. J. Geophys. Res.,99, 8109–8124.

  • Garcia, R. R., and S. Solomon, 1985: The effect of breaking gravity waves on the dynamics and chemical composition of the mesosphere and lower thermosphere. J. Geophys. Res.,90, 3850–3868.

  • Hines, C. O., 1991: The saturation of gravity waves in the middle atmosphere. Part I: Critique of linear-instability theory. J. Atmos. Sci.,48, 1348–1359.

  • ——, 1997: Doppler-spread parameterization of gravity-wave momentum deposition in the middle atmosphere. 1. Basic formulation. J. Atmos. Sol.-Terr. Phys.,59, 371–86.

  • Holton, J. R., 1982: The role of gravity wave induced drag and diffusion in the momentum budget of the mesosphere. J. Atmos. Sci.,39, 791–799.

  • ——, and R. S. Lindzen, 1972: An updated theory for the quasi-biennial cycle of the tropical stratosphere. J. Atmos. Sci.,29, 1076–1080.

  • Jackson, D. R., and L. J. Gray, 1994: Simulation of the semi-annual oscillation of the equatorial middle atmosphere using the Extended UGAMP General Circulation Model. Quart. J. Roy. Meteor. Soc.,120, 1559–1588.

  • Kiehl, J. T., J. J. Hack, G. B. Bonan, B. A. Boville, B. P. Briegleb, D. L. Williamson, and P. J. Rasch, 1996: Description of the NCAR Community Climate Model (CCM3). NCAR Tech. Note 420, 152 pp. [Available from NCAR, P.O. Box 3000, Boulder, CO 80307-3000.].

  • Klinker, E., and P. D. Sardeshmukh, 1992: The diagnosis of mechanical dissipation in the atmosphere from large-scale balance requirements. J. Atmos. Sci.,49, 608–627.

  • Lelong, M.-P., and T. J. Dunkerton, 1998a: Inertia–gravity wave breaking in three dimensions. Part I: Convectively stable waves. J. Atmos. Sci.,55, 2473–2488.

  • ——, and ——, 1998b: Inertia–gravity wave breaking in three dimensions. Part II: Convectively unstable waves. J. Atmos. Sci.,55, 2489–2501.

  • Lighthill, J., 1978: Waves in Fluids. Cambridge University Press, 504 pp.

  • Lindzen, R. S., 1981: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res.,86, 9707–9714.

  • ——, 1985: Multiple gravity-wave breaking levels. J. Atmos. Sci.,42, 301–305.

  • ——, and J. R. Holton, 1968: A theory of the quasi-biennial oscillation. J. Atmos. Sci.,25, 1095–1107.

  • Marks, C. J., and S. D. Eckermann, 1995: A three-dimensional nonhydrostatic ray-tracing model for gravity waves: Formulation and preliminary results for the middle atmosphere. J. Atmos. Sci.,52, 1959–1984.

  • McFarlane, N. A., 1987: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci.,44, 1775–1800.

  • McIntyre, M. E., 1989: On dynamics and transport near the polar mesopause in summer. J. Geophys. Res.,94, 14 617–14 628.

  • Medvedev, A. S., and G. P. Klaassen, 1995: Vertical evolution of gravity wave spectra and the parameterization of associated wave drag. J. Geophys. Res.,100, 25 841–25 853.

  • Murayama, Y., T. Tsuda, and S. Fukao, 1994: Seasonal variation of gravity wave activity in the lower atmosphere observed with the MU radar. J. Geophys. Res.,99, 23 057–23 069.

  • Nance, L. B., and D. R. Durran, 1997: A modeling study of nonstationary trapped mountain lee waves. Part I: Mean flow variability. J. Atmos. Sci.,54, 2275–2291.

  • Norton, W. A., and J. Thuburn, 1996: The two-day wave in a middle atmosphere 6CM. Geophys. Res. Lett.,23, 2113–2116.

  • O’Sullivan, D., and T. J. Dunkerton, 1995: Generation of inertia-gravity waves in a simulated life cycle of baroclinic instability. J. Atmos. Sci.,52, 3695–3716.

  • Palmer, T. N., G. J. Shutts, and R. Swinbank, 1986: Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parameterization. Quart. J. Roy. Meteor. Soc.,112, 1001–1039.

  • Pfister, L., and Coauthors, 1993: Gravity waves generated by a tropical cyclone during the STEP tropical field program: A case study. J. Geophys. Res.,98, 8611–8638.

  • Pitteway, M. L. V., and C. O. Hines, 1963: The viscous damping of atmospheric gravity waves. Can. J. Phys.,41, 1935–1948.

  • Prichard, I. T., and L. Thomas, 1993: Radar observations of gravity-wave momentum fluxes in the troposphere and lower stratosphere. Ann. Geophys.,11, 1075–1083.

  • ——, ——, and R. M. Worthington, 1995: The characteristics of mountain waves observed by radar near the west coast of Wales. Ann. Geophys.,13, 757–767.

  • Prusa, J., P. K. Smolarkiewicz, and R. R. Garcia, 1996: Propagation and breaking at high altitudes of gravity waves excited by tropospheric forcing. J. Atmos. Sci.,53, 2186–2216.

  • Ray, E. A., M. J. Alexander, and J. R. Holton, 1998: An analysis of the structure and forcing of the equatorial semiannual oscillation in zonal wind. J. Geophys. Res.,103, 1759–1774.

  • Reeder, M. J., and M. Griffiths, 1996: Stratospheric inertia-gravity waves generated in a numerical model of frontogenesis. II: Wave sources and generation mechanisms. Quart. J. Roy. Meteor. Soc.,122, 1175–1195.

  • Rind, D., R. Suozzo, and N. K. Balachandran, 1988: The GISS global climate–middle atmosphere model. Part II: Model variability due to interactions between planetary waves, the mean circulation and gravity wave drag. J. Atmos. Sci.,45, 371–386.

  • Sato, K., 1990: Vertical wind disturbances in the troposphere and lower stratosphere observed by the MU radar. J. Atmos. Sci.,47, 2803–2817.

  • ——, 1992: Vertical wind disturbances in the afternoon of mid-summer revealed by the MU radar. Geophys. Res. Lett.,19, 1943–1946.

  • ——, 1993: Small-scale wind disturbances observed by the MU radar during the passage of Typhoon Kelly. J. Atmos. Sci.,50, 518–537.

  • ——, 1994: A statistical study of the structure, saturation and sources of inertio-gravity waves in the lower stratosphere observed with the MU radar. J. Atmos. Terr. Phys.,56, 755–774.

  • ——, and M. Yamada, 1994: Vertical structure of atmospheric gravity waves revealed by the wavelet analysis. J. Geophys. Res.,99, 20 623– 20 631.

  • ——, and T. J. Dunkerton, 1997: Estimates of momentum flux associated with equatorial Kelvin and gravity waves. J. Geophys. Res.,102, 26 247–26 261.

  • ——, F. Hasegawa, and I. Hirota, 1994: Short-period disturbances in the equatorial lower stratosphere. J. Meteor. Soc. Japan,72, 859–872.

  • ——, D. O’Sullivan, and T. J. Dunkerton, 1997: Low-frequency inertia-gravity waves in the stratosphere revealed by three-week continuous observation with the MU radar. Geophys. Res. Lett.,24, 1739–1742.

  • Smith, S. A., D. C. Fritts, and T. E. VanZandt, 1987: Evidence for a saturated spectrum of atmospheric gravity waves. J. Atmos. Sci.,44, 1404–1410.

  • Swenson, G. R., and P. J. Espy, 1995: Observations of two-dimensional airglow structure and Na density from the ALOHA, October 9, 1993, “Storm Flight.” Geophys. Res. Lett.,22, 2845–2848.

  • Taylor, M. J., Y. Y. Gu, X. Tao, C. S. Gardner, and M. B. Bishop, 1995: An investigation of intrinsic gravity wave signatures using coordinated lidar and nightglow image measurements. Geophys. Res. Lett.,22, 2853–2856.

  • Warner, C. D., and M. E. McIntyre, 1996: On the propagation and dissipation of gravity wave spectra through a realistic middle atmosphere. J. Atmos. Sci.,53, 3213–3235.

  • Worthington, R. M., and L. Thomas, 1998: The frequency spectrum of mountain waves. Quart. J. Roy. Meteor. Soc.,124, 687–703.

  • Zhu, X., 1994: A new theory of the saturated gravity wave spectrum for the middle atmosphere. J. Atmos. Sci.,51, 3615–3626.

  • ——, and J. R. Holton, 1987: Mean fields induced by local gravity-wave forcing in the middle atmosphere. J. Atmos. Sci.,44, 620–630.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 152 152 14
PDF Downloads 44 44 9

A Spectral Parameterization of Mean-Flow Forcing due to Breaking Gravity Waves

View More View Less
  • 1 Colorado Research Associates, Boulder, Colorado
  • | 2 NorthWest Research Associates, Bellevue, Washington
© Get Permissions
Restricted access

Abstract

A spectral parameterization of mean-flow forcing due to breaking gravity waves is described for application in the equations of motion in atmospheric models. The parameterization is based on linear theory and adheres closely to fundamental principles of conservation of wave action flux, linear stability, and wave–mean-flow interaction. Because the details of wave breakdown and nonlinear interactions are known to be very complex and are still poorly understood, only the simplest possible assumption is made: that the momentum fluxes carried by the waves are deposited locally and entirely at the altitude of linear wave breaking. This simple assumption allows a straightforward mapping of the momentum flux spectrum, input at a specified source altitude, into vertical profiles of mean-flow force. A coefficient of eddy diffusion can also be estimated. The parameterization can be used with any desired input spectrum of momentum flux. The results are sensitive to the details of this spectrum and also realistically sensitive to the background vertical shear and stability profiles. These sensitivities make the parameterization ideally suited for studying both the effects of gravity waves from unique sources like topography and convection as well as generalized broad input spectra. Existing constraints on input parameters are also summarized from the available observations. With these constraints, the parameterization generates realistic variations in gravity-wave-driven, mean-flow forcing.

Corresponding author address: Dr. M. Joan Alexander, Colorado Research Associates, 3380 Mitchell Lane, Boulder, CO 80301.

Email: alexand@colorado-research.com

Abstract

A spectral parameterization of mean-flow forcing due to breaking gravity waves is described for application in the equations of motion in atmospheric models. The parameterization is based on linear theory and adheres closely to fundamental principles of conservation of wave action flux, linear stability, and wave–mean-flow interaction. Because the details of wave breakdown and nonlinear interactions are known to be very complex and are still poorly understood, only the simplest possible assumption is made: that the momentum fluxes carried by the waves are deposited locally and entirely at the altitude of linear wave breaking. This simple assumption allows a straightforward mapping of the momentum flux spectrum, input at a specified source altitude, into vertical profiles of mean-flow force. A coefficient of eddy diffusion can also be estimated. The parameterization can be used with any desired input spectrum of momentum flux. The results are sensitive to the details of this spectrum and also realistically sensitive to the background vertical shear and stability profiles. These sensitivities make the parameterization ideally suited for studying both the effects of gravity waves from unique sources like topography and convection as well as generalized broad input spectra. Existing constraints on input parameters are also summarized from the available observations. With these constraints, the parameterization generates realistic variations in gravity-wave-driven, mean-flow forcing.

Corresponding author address: Dr. M. Joan Alexander, Colorado Research Associates, 3380 Mitchell Lane, Boulder, CO 80301.

Email: alexand@colorado-research.com

Save