Theoretical and Computational Fluid Dynamics

, Volume 20, Issue 5–6, pp 501–524

Structure of tropical variability from a vertical mode perspective

Original Article


A composite mesoscale precipitation event and a convectively coupled Kelvin wave produced by a diabatically accelerated cloud resolving model are compared. Special emphasis is placed on the vertical structure of density and moisture perturbations and the interaction of these perturbations with the composited dynamical fields. Both composites share the same general features, a gradual deepening and strengthening of convection followed by deep convection and a stratiform region, quite similar in character to observations and some recent idealized models. Composited frozen moist static energy (FMSE) perturbations are several times larger than virtual temperature perturbations, suggesting moisture is a dominant regulator of convection. An empirically derived two vertical mode decomposition of the dynamical and moisture fields is found to reproduce both composites quite well. The leading vertical modes of FMSE and virtual temperature variability are strongly correlated with the modes of vertical velocity variability; these correlations are strongest at near-zero time lags. Deep convection is associated with moistening in the lower and middle troposphere, while shallow convection is associated with a moist lower troposphere and dry middle and upper troposphere. To the extent that our numerical model is realistic, the empirical modal decomposition provides support for the use of two-mode idealized models for convective interaction with large-scale circulations and guidance for formulating feedbacks between convection and the thermodynamic profile in such models. The FMSE budget leads to an interpretation of the convective life-cycle as a recharge–discharge mechanism in column-integrated FMSE. The budget analysis places diabatic forcing, surface and radiative fluxes into the moist energetic framework. In particular, these fluxes are seen to prolong active convection, but play a passive role in its initiation. The modally decomposed FMSE budget highlights the dynamical importance of the second baroclinic mode in moistening the lower and middle troposphere before convective onset (recharging), and then discharging stored FMSE in the stratiform region.


Tropical meteorology Atmospheric convection Mesoscale convective system Kelvin wave 


92.60.Ek 92.60.Jq 92.60.Nv 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Blossey, P.N., Bretherton, C.S., Cetrone, J., Kharoutdinov, M.: Cloud-resolving model simulations of KWAJEX: model sensitivities and comparisions with satellite and radar observations. J. Atmos. Sci. (accepted, 2006)Google Scholar
  2. 2.
    Bretherton, C.S., Blossey, P.N., Peters, M.E.: Interpretation if simple and cloud-resolving models of moist convection–radiation interaction with a mock-Walker circulation. Theor. Comp. Fluid Dyn. (in press, 2005)Google Scholar
  3. 3.
    Bretherton C.S., Peters M.E., Back L.E. (2004). Relationships between water vapor path and precipitation over the tropical oceans. J. Climate 17:1517–1528CrossRefADSGoogle Scholar
  4. 4.
    Carr M.T., Bretherton C.S. (2001). Convective momentum transport over the tropical Pacific: budget estimates. J. Atmos. Sci. 58:1673–1693CrossRefADSGoogle Scholar
  5. 5.
    Emanuel K.A., Neelin J.D., Bretherton C.S. (1994). On large-scale circulations in convecting atmospheres. Quart. J. Roy. Meteorol. Soc. 120:1111–1143CrossRefADSGoogle Scholar
  6. 6.
    Fulton S.R., Schubert W.H. (1985). Vertical normal mode transforms: theory and application. Mon. Wea. Rev. 113:647–658CrossRefGoogle Scholar
  7. 7.
    Grabowski W.W. (2001). Coupling cloud processes with the large-scale dynamics using the cloud-resolving convection parameterization (CRCP). J. Atmos. Sci. 58:978–997CrossRefADSGoogle Scholar
  8. 8.
    Haertel P.T., Kiladis G.N. (2004). Dynamics of 2-day equatorial waves. J. Atmos. Sci. 61:2707–2721CrossRefADSGoogle Scholar
  9. 9.
    Houze, R.A.: Cloud dynamics. Academic Press (1993)Google Scholar
  10. 10.
    Khairoutdinov M.F., Randall D.A. (2003). Cloud resolving modeling of the ARM Summer 1997 IOP: model formulation, results, uncertainties, and sensitivities. J. Atmos. Sci. 60:607–625CrossRefADSGoogle Scholar
  11. 11.
    Khouider, B., Majda, A.J.: Model multicloud parameterizations for convectively coupled waves: detailed nonlinear wave evolution. Dyn. Atmos. Ocean. (accepted, 2005)Google Scholar
  12. 12.
    Khouider, B., Majda, A.J.: Multicloud convective parameterizations with crude vertical structure. Theor. Comp. Fluid Dyn. (in press, 2005)Google Scholar
  13. 13.
    Khouider B., Majda A.J. (2006). A simple multicloud parameterization for convectively coupled tropical waves. Part I: linear analysis. J. Atmos. Sci. 63(4):1308–1323MathSciNetADSGoogle Scholar
  14. 14.
    Khouider, B., Majda, A.J.: A simple multicloud parameterization for convectively coupled tropical waves. Part II: nonlinear simulations. J. Atmos. Sci. (accepted, 2005)Google Scholar
  15. 15.
    Kuang Z., Blossey P.N., Bretherton C.S. (2005). A new approach for 3D cloud resolving simulations of large scale atmospheric circulations. Geophys. Res. Letts. 32:L02–809. DOI 10.1029/2004GL021,024CrossRefGoogle Scholar
  16. 16.
    Kuang, Z., Bretherton, C.S.: A mass flux scheme view of a high-resolution simulation of transition from shallow to deep cumulus convection. J. Atmos. Sci. (in press, 2006)Google Scholar
  17. 17.
    Lin J.L., Zhang M., Mapes B. (2005). Zonal momentum budget of the Madden-Julian Oscillation: the source and strength of equivalent linear damping. J. Atmos. Sci. 62:2172–2188CrossRefADSGoogle Scholar
  18. 18.
    Madden R.A., Julian P.R. (1972). Description of global-scale circulation cells in the tropics with a 40–50 day period. J. Atmos. Sci. 29:1109–1123CrossRefADSGoogle Scholar
  19. 19.
    Majda A.J., Khouider B., Kiladis G.N., Straub K.H., Shefter M.G. (2004). A model for convectively coupled tropical waves: nonlinearity, rotation, and comparison with observations. J. Atmos. Sci. 61:2188–2205MathSciNetCrossRefADSGoogle Scholar
  20. 20.
    Maloney E.D., Hartmann D.L. (1998). Frictional moisture convergence in a composite life cycle of the Madden–Julian oscillation. J. Clim. 11:2387–2403CrossRefADSGoogle Scholar
  21. 21.
    Mapes, B., Tulich, S., Lin, J., Zuidema, P.: The mesoscale convection life cycle: building block or prototype for large-scale tropical waves? Dyn. Atmos. Ocean. (in press, 2006)Google Scholar
  22. 22.
    Mapes B.E. (2000). Convective inhibition, subgridscale triggering, and stratiform instability in a toy tropical wave model. J. Atmos. Sci. 57:1515–1535CrossRefADSGoogle Scholar
  23. 23.
    Mapes B.E. (2004). Sensitivities of cumulus-ensemble rainfall in a cloud-resolving model with parameterized large-scale dynamics. J. Atmos. Sci. 61:2308–2317CrossRefADSGoogle Scholar
  24. 24.
    Matsuno T. (1966). Quasi-geostrophic motions in the equatorial area. J. Meteorol. Soc. Jpn 44:25–42Google Scholar
  25. 25.
    Moskowitz B.M., Bretherton C.S. (2000). An analysis of frictional feedback on a moist equatorial Kelvin mode. J. Atmos. Sci. 57:2188–2206CrossRefADSGoogle Scholar
  26. 26.
    Neelin J.D., Held I.M. (1987). Modeling tropical convergence based on the moist static energy budget. Mon. Weather. Rev. 115:3–12CrossRefGoogle Scholar
  27. 27.
    Pauluis, O., Frierson, D., Garner, S., Held, I., Vallis, G: The hypohydrostatic rescaling and its impacts on atmospheric convection. Theor. Comp. Fluid Dyn. (submitted, 2006)Google Scholar
  28. 28.
    Sherwood S.C. (1999). Convective precursors and predictability in the tropical west Pacific. Mon. Weather. Rev. 127:2977–2991CrossRefGoogle Scholar
  29. 29.
    Sherwood S.C., Wahrlich R. (1999). Observed evolution of tropical deep convective events and their environment. Mon. Weather. Rev. 127:1777–1795CrossRefGoogle Scholar
  30. 30.
    Straub K.H., Kiladis G.N. (2003). The observed structure of convectively coupled kelvin waves: comparison with simple models of coupled wave instability. J. Atmos. Sci. 60:1655–1668MathSciNetCrossRefADSGoogle Scholar
  31. 31.
    Tomita H., Miura H., Iga S., Nasuno T., Satoh M. (2005). A global cloud-resolving simulation: preliminary results from an aqua planet experiment. J. Geophys. Res. 32:L08–805, DOI 10.1029/2005GL022,459Google Scholar
  32. 32.
    Trenberth K.E., Stepaniak D.P. (2003). Covariability of components of poleward atmospheric energy transports on seasonal and interannual timescales. J. Clim. 16:3691–3705CrossRefADSGoogle Scholar
  33. 33.
    Wang B. (1988). Dynamics of tropical low-frequency waves: an analysis of the moist Kelvin wave. J. Atmos. Sci. 45:2051–2065CrossRefADSGoogle Scholar
  34. 34.
    Wheeler M., Kiladis G.N. (1999). Convectively coupled equatorial waves: analysis of clouds and temperature in the wavenumber–frequency domain. J. Atmos. Sci. 56:374–399CrossRefADSGoogle Scholar
  35. 35.
    Wheeler M., Kiladis G.N., Webster P.J. (2000). Large-scale dynamical fields associated with convectively coupled waves. J. Atmos. Sci. 57:613–640CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Matthew E. Peters
    • 1
    • 2
  • Christopher S. Bretherton
    • 3
  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of Earth and Planetary SciencesHarvard UniversityCambridgeUSA
  3. 3.Atmospheric Science DepartmentUniversity of WashingtonSeattleUSA

Personalised recommendations