Theoretical and Computational Fluid Dynamics

, Volume 20, Issue 5–6, pp 351–375 | Cite as

Multicloud Convective Parametrizations with Crude Vertical Structure

  • Boualem Khouider
  • Andrew J. Majda
Original Article


Recent observational analysis reveals the central role of three multi-cloud types, congestus, stratiform, and deep convective cumulus clouds, in the dynamics of large scale convectively coupled Kelvin waves, westward propagating two-day waves, and the Madden–Julian oscillation. The authors have recently developed a systematic model convective parametrization highlighting the dynamic role of the three cloud types through two baroclinic modes of vertical structure: a deep convective heating mode and a second mode with low level heating and cooling corresponding respectively to congestus and stratiform clouds. The model includes a systematic moisture equation where the lower troposphere moisture increases through detrainment of shallow cumulus clouds, evaporation of stratiform rain, and moisture convergence and decreases through deep convective precipitation and a nonlinear switch which favors either deep or congestus convection depending on whether the troposphere is moist or dry. Here several new facets of these multi-cloud models are discussed including all the relevant time scales in the models and the links with simpler parametrizations involving only a single baroclinic mode in various limiting regimes. One of the new phenomena in the multi-cloud models is the existence of suitable unstable radiative convective equilibria (RCE) involving a larger fraction of congestus clouds and a smaller fraction of deep convective clouds. Novel aspects of the linear and nonlinear stability of such unstable RCE’s are studied here. They include new modes of linear instability including mesoscale second baroclinic moist gravity waves, slow moving mesoscale modes resembling squall lines, and large scale standing modes. The nonlinear instability of unstable RCE’s to homogeneous perturbations is studied with three different types of nonlinear dynamics occurring which involve adjustment to a steady deep convective RCE, periodic oscillation, and even heteroclinic chaos in suitable parameter regimes.


Intermediate convective parametrizations Multicloud models Moist gravity waves Tropical convection Convective instability Bifurcation Periodic solutions Heteroclinic orbits Congestus clouds Stratiform clouds Deep convective clouds 


92.60 92.60 92.60 02.30 202.60 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Nakazawa T. (1988) Tropical super clusters within intraseasonal variations over the western pacific. J. Meteorol. Soc. Jpn. 66, 823–839Google Scholar
  2. 2.
    Hendon H.H., Liebmann B. (1994) Organization of convection within the Madden–Julian oscillation. J. Geophys. Res. 99, 8073–8083CrossRefADSGoogle Scholar
  3. 3.
    Wheeler M., Kiladis G.N. (1999) Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber-frequency domain. J. Atmos. Sci. 57, 613–640CrossRefADSGoogle Scholar
  4. 4.
    Emanuel, K.A., Raymond, D.J. The representation of Cumulus convection in numerical models. In: Meteorological monographs, vol. 84, Boston: American Meterological Society, 1993Google Scholar
  5. 5.
    Smith R.K (1997) The physics and parametrization of moist atmospheric convection. NATO ASI, Kluwer, DordrechtGoogle Scholar
  6. 6.
    Slingo J.M. et al. (1996) Intraseasonal oscillation in 15 atmospheric general circulation models: results from an amip diagnostic subproject. Climate Dyn. 12, 325–357CrossRefADSGoogle Scholar
  7. 7.
    Moncrieff M.W., Klinker E. (1997) Organized convective systems in the tropical western pacific as a process in general circulation models: a toga-coare case study. Q. J. Roy. Meteorol. Soc. 123, 805–827CrossRefADSGoogle Scholar
  8. 8.
    Emanuel K.A. (1987) An air-sea interaction model of intraseasonal oscillations in the tropics. J. Atmos. Sci. 44, 2324–2340CrossRefADSGoogle Scholar
  9. 9.
    Mapes B.E. (1993) Gregarious tropical convection. J. Atmos. Sci. 50, 2026–2037CrossRefADSGoogle Scholar
  10. 10.
    Neelin D., Yu J. (1994) Modes of tropical variability under convective adjustment and the Madden–Julian oscillation. Part I: analytical theory. J. Atmos. Sci. 51, 1876–1894CrossRefADSGoogle Scholar
  11. 11.
    Yano J.-I., McWilliams J., Moncrieff M., Emanuel K.A. (1995) Hierarchical tropical cloud systems in an analog shallow-water model. J. Atmos. Sci. 48, 1723–1742CrossRefADSGoogle Scholar
  12. 12.
    Yano J.-I., Moncrieff M., McWilliams J. (1998) Linear stability and single-column analyses of several cumulus parametrization categories in a shallow-water model. Q. J. Roy. Meteorol. Soc. 124, 983–1005CrossRefADSGoogle Scholar
  13. 13.
    Majda A., Shefter M. (2001) Waves and instabilities for model tropical convective parametrizations. J. Atmos. Sci. 58, 896–914MathSciNetCrossRefADSGoogle Scholar
  14. 14.
    Majda A.J., Khouider B. (2002) Stochastic and mesoscopic models for tropical convection. Proc. Natl. Acad. Sci. USA 99, 1123–1128MATHCrossRefADSGoogle Scholar
  15. 15.
    Fuchs Z., Raymond D. (2002) Large-scale modes of a nonrotating atmosphere with water vapor and cloud-radiation feedbacks. J. Atmos. Sci. 59, 1669–1679CrossRefADSGoogle Scholar
  16. 16.
    Frierson D., Majda A., Pauluis O. (2004) Dynamics of precipitation fronts in the tropical atmosphere: a novel relaxation limit. Commun. Math. Sci. 2, 591–626MATHMathSciNetGoogle Scholar
  17. 17.
    Charney J.G., Eliassen A. (1964) On the growth of the hurricane depression. J. Atmos. Sci. 21, 68–75CrossRefADSGoogle Scholar
  18. 18.
    Yamasaki M. (1969) Large-scale disturbances in a conditionally unstable atmosphere in low latitudes. Pap. Meteor. Geophys. 20, 289–336Google Scholar
  19. 19.
    Hayashi Y. (1971) Large-scale equatorial waves destabilized by convective heating in the presence of surface friction. J. Meteor. Soc. Jpn. 49, 458–466Google Scholar
  20. 20.
    Lindzen R.S. (1974) Wave-cisk in the tropics. J. Atmos. Sci. 31, 156–179CrossRefADSGoogle Scholar
  21. 21.
    Arakawa A., Shubert W.H. (1974) Interaction of a cumulus cloud ensemble with the large-scale environment. Part i. J. Atmos. Sci. 31, 674–701CrossRefADSGoogle Scholar
  22. 22.
    Emanuel K.A., Neelin J.D., Bretherton C.S. (1994) On large-scale circulations in convecting atmosphere. Q. J. Roy. Meteor. Soc. 120, 1111–1143CrossRefADSGoogle Scholar
  23. 23.
    Lin X., Johnson R.H. (1996) Kinematic and thermodynamic characteristics of the flow over the western pacific warm pool during toga coare. J. Atmos. Sci. 53, 695–715CrossRefADSGoogle Scholar
  24. 24.
    Johnson R.H., Rickenbach T.M., Rutledge S.A., Ciesielski P.E., Schubert W.H. (1999) Trimodal characteristics of tropical convection. J. Climate 12, 2397–2407CrossRefADSGoogle Scholar
  25. 25.
    Straub K.H., Kiladis G.N. (2002) Observations of a convectively-coupled kelvin wave in the eastern pacific itcz. J. Atmos. Sci. 59, 30–53CrossRefADSGoogle Scholar
  26. 26.
    Haertl P.T., Kiladis G.N. (2004) On the dynamics of two day equatorial disturbances. J. Atmos. Sci. 61, 2707–2721CrossRefADSGoogle Scholar
  27. 27.
    Kiladis G.N., Straub K.H., Haertl P. (2005) Zonal and vertical structure of the Madden–Julian oscillation. J. Atmos. Sci. 62, 2790–2809CrossRefADSGoogle Scholar
  28. 28.
    Dunkerton T.J., Crum F.X. (1995) Eastward propagating 2- to 15-day equatorial convection and its relation to the tropical intraseasonal oscillation. J. Geophys. Res. 100, 25781–25790CrossRefADSGoogle Scholar
  29. 29.
    Majda A., Biello J. (2004) A multi-scale model for the intraseasonal oscillation. Proc. Natl. Acad. Sci. 101, 4736–4741MATHMathSciNetCrossRefADSGoogle Scholar
  30. 30.
    Biello J., Majda A. (2005) A multi-scale model for the madden–julian oscillation. J. Atmos. Sci. 62, 1694–1721MathSciNetCrossRefADSGoogle Scholar
  31. 31.
    Zehnder J. (2001) A comparison of convergence- and surface-flux-based convective parametrizations with applications to tropical cyclogenesis. J. Atmos. Sci. 58, 283–301CrossRefADSGoogle Scholar
  32. 32.
    Craig G.C., Gray S.L. (1996) CISK or WISHE as the mechanism for tropical cyclone intensification. J. Atmos. Sci. 53, 3528–3540CrossRefADSGoogle Scholar
  33. 33.
    Mapes B.E. (2000) Convective inhibition, subgridscale triggering energy, and “stratiform instability” in a toy tropical wave model. J. Atmos. Sci. 57, 1515–1535CrossRefADSGoogle Scholar
  34. 34.
    Majda A., Shefter M. (2001) Models for stratiform instability and convectively coupled waves. J. Atmos. Sci. 58, 1567–1584MathSciNetCrossRefADSGoogle Scholar
  35. 35.
    Majda A., Khouider B., Kiladis G.N., Straub K.H., Shefter M. (2004) A model for convectively coupled tropical waves: nonlinearity, rotation, and comparison with observations. J. Atmos. Sci. 61, 2188–2205MathSciNetCrossRefADSGoogle Scholar
  36. 36.
    Yano J.-I., Emanuel K. (1991) An improved model of the equatorial troposphere and its coupling to the stratosphere. J. Atmos. Sci. 18, 377–389CrossRefADSGoogle Scholar
  37. 37.
    Khouider B., Majda A.J. (2006). A simple multicloud parametrization for convectively coupled tropical waves. Part i: linear analysis. J. Atmos. Sci. 63, 1308–1323MathSciNetADSGoogle Scholar
  38. 38.
    Khouider, B., Majda, A.J. A simple multicloud parametrization for convectively coupled tropical waves. Part ii: nonlinear simulations. J. Atmos. Sci. (2006, in press)Google Scholar
  39. 39.
    Khouider, B., Majda, A.J. Model multicloud parametrizations for convectively coupled waves: detailed nonlinear wave evolution. Dynam. Atmos. Oceans (2006, in press)Google Scholar
  40. 40.
    Neelin D., Zeng N. (2000) A quasi-equilibrium tropical circulation model–formulation. J. Atmos. Sci. 57, 1741–1766CrossRefADSGoogle Scholar
  41. 41.
    Majda A., Biello J. (2003) The nonlinear interaction of barotropic and equatorial baroclinic Rossby waves. J. Atmos. Sci. 60, 1809–1821MathSciNetCrossRefADSGoogle Scholar
  42. 42.
    Khouider B., Majda A.J. (2005) A non-oscillatory well balanced scheme for an idealized tropical climate model. Part I: Algorithm and validation. Theor. Comput. Fluid Dyn. 19, 331–354CrossRefGoogle Scholar
  43. 43.
    Khouider B., Majda A.J. (2005) A non-oscillatory well balanced scheme for an idealized tropical climate model. Part II: Nonlinear coupling and moisture effects. Theor. Comput. Fluid Dyn. 19, 355–375CrossRefGoogle Scholar
  44. 44.
    Gill A. (1982) Atmosphere-ocean dynamics. International geophysics series, vol. 30. Academic, New YorkGoogle Scholar
  45. 45.
    Betts A.K., Miller M.J. (1986) A new convective adjustemnt scheme. Part ii: single column tests using gate wave, bomex, and arctic air-mass data sets. Q. J. Roy. Meteorol. Soc. 112, 693–709CrossRefADSGoogle Scholar
  46. 46.
    Emanuel K. (1994) Atmospheric convection. Oxford University Press, OxfordGoogle Scholar
  47. 47.
    Betts A.K. (1986) A new convective adjustemnt scheme. part i: Observational and theoretical basis. Q. J. Roy. Meteorol. Soc. 112, 677–692CrossRefADSGoogle Scholar
  48. 48.
    Bretherton C.S., Peters M.E., Back L.E. (2004) Relationship between water vapor path and precipitation over the tropical oceans. J. Climate 17, 1517–1528CrossRefADSGoogle Scholar
  49. 49.
    Armbuster D.J., Guckenheimer J., Holmes P. (1988) Heteroclinic cycles and modulated traveling waves in systems with \(\mathcal{O}(2)\) symmetry. Phys. D 29, 257–282MathSciNetCrossRefADSGoogle Scholar
  50. 50.
    Holmes P., Lumley J.L., Berkooz G. (1996) Turbulence, coherent structures, dynamical systems, and symmetry. Cambridge University Press, New YorkMATHGoogle Scholar
  51. 51.
    Pruppacher H.R, Klett J.D. (2000) Microphysics of clouds and precipitation, chap 12. Kluwer, DordrechtGoogle Scholar
  52. 52.
    Lin J., Neelin J.D., Zeng N. (2000) Maintenance of tropical intraseasonal variability: Impact of evaporation-wind feedback and midlatitude storms. J. Atmos. Sci. 57, 2793–2823CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  2. 2.Department of Mathematics and Center for Atmosphere/Ocean Sciences, Courant InstituteNew York UniversityNew YorkUSA

Personalised recommendations