A Simple Multicloud Parameterization for Convectively Coupled Tropical Waves. Part II: Nonlinear Simulations

Boualem Khouider Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

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Andrew J. Majda Department of Mathematics, and Center for Atmosphere Ocean Science, Courant Institute, New York University, New York, New York

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Abstract

Observations in the Tropics point to the important role of three cloud types, congestus, stratiform, and deep convective clouds, besides ubiquitous shallow boundary layer clouds for both the climatology and large-scale organized anomalies such as convectively coupled Kelvin waves, two-day waves, and the Madden–Julian oscillation. Recently, the authors have developed a systematic model convective parameterization 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 lower troposphere heating and cooling corresponding respectively to congestus and stratiform clouds. The model includes both 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 also a nonlinear switch that favors either deep or congestus convection depending on whether the lower middle troposphere is moist or dry. Here these model convective parameterizations are applied to a 40 000-km periodic equatorial ring without rotation, with a background sea surface temperature (SST) gradient and realistic radiative cooling mimicking a tropical warm pool. Both the emerging “Walker cell” climatology and the convectively coupled wave fluctuations are analyzed here while various parameters in the model are varied. The model exhibits weak congestus moisture coupled waves outside the warm pool in a turbulent bath that intermittently amplify in the warm pool generating convectively coupled moist gravity wave trains propagating at speeds ranging from 15 to 20 m s−1 over the warm pool, while retaining a classical Walker cell in the mean climatology. The envelope of the deep convective events in these convectively coupled wave trains often exhibits large-scale organization with a slower propagation speed of 3–5 m s−1 over the warm pool and adjacent region. Occasional much rarer intermittent deep convection also occurs outside the warm pool. The realistic parameter regimes in the multicloud model are identified as those with linearized growth rates for large scale instabilities roughly in the range of 0.5 K day−1.

Corresponding author address: Dr. Boualem Khouider, Mathematics and Statistics, University of Victoria, P.O. Box 3045 STN CSC, Victoria, BC V8W 3P4, Canada. Email: khouider math.uvic.ca

Abstract

Observations in the Tropics point to the important role of three cloud types, congestus, stratiform, and deep convective clouds, besides ubiquitous shallow boundary layer clouds for both the climatology and large-scale organized anomalies such as convectively coupled Kelvin waves, two-day waves, and the Madden–Julian oscillation. Recently, the authors have developed a systematic model convective parameterization 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 lower troposphere heating and cooling corresponding respectively to congestus and stratiform clouds. The model includes both 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 also a nonlinear switch that favors either deep or congestus convection depending on whether the lower middle troposphere is moist or dry. Here these model convective parameterizations are applied to a 40 000-km periodic equatorial ring without rotation, with a background sea surface temperature (SST) gradient and realistic radiative cooling mimicking a tropical warm pool. Both the emerging “Walker cell” climatology and the convectively coupled wave fluctuations are analyzed here while various parameters in the model are varied. The model exhibits weak congestus moisture coupled waves outside the warm pool in a turbulent bath that intermittently amplify in the warm pool generating convectively coupled moist gravity wave trains propagating at speeds ranging from 15 to 20 m s−1 over the warm pool, while retaining a classical Walker cell in the mean climatology. The envelope of the deep convective events in these convectively coupled wave trains often exhibits large-scale organization with a slower propagation speed of 3–5 m s−1 over the warm pool and adjacent region. Occasional much rarer intermittent deep convection also occurs outside the warm pool. The realistic parameter regimes in the multicloud model are identified as those with linearized growth rates for large scale instabilities roughly in the range of 0.5 K day−1.

Corresponding author address: Dr. Boualem Khouider, Mathematics and Statistics, University of Victoria, P.O. Box 3045 STN CSC, Victoria, BC V8W 3P4, Canada. Email: khouider math.uvic.ca

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  • Bretherton, C. B., and A. H. Sobel, 2002: A simple model of a convectively coupled Walker circulation using the weak temperature gradient approximation. J. Climate, 15 , 29072920.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C. B., M. E. Peters, and L. E. Back, 2004: Relationship between water vapor path and precipitation over the tropical oceans. J. Climate, 17 , 15171528.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., and A. Eliassen, 1964: On the growth of the hurricane depression. J. Atmos. Sci., 21 , 6875.

  • Craig, G. C., and S. L. Gray, 1996: CISK or WISHE as the mechanism for tropical cyclone intensification. J. Atmos. Sci., 53 , 35283540.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T. J., and F. X. Crum, 1995: Eastward propagating 2- to 15-day equatorial convection and its relation to the tropical intraseasonal oscillation. J. Geophys. Res., 100 , 2578125790.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1987: An air–sea interaction model of intraseasonal oscillations in the tropics. J. Atmos. Sci., 44 , 23243240.

  • Emanuel, K. A., J. D. Neelin, and C. S. Bretherton, 1994: On large-scale circulations in convecting atmosphere. Quart. J. Roy. Meteor. Soc., 120 , 11111143.

    • Search Google Scholar
    • Export Citation
  • Fuchs, Z., and D. Raymond, 2002: Large-scale modes of a nonrotating atmosphere with water vapor and cloud-radiation feedbacks. J. Atmos. Sci., 59 , 16691679.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 666 pp.

  • Grabowski, W. W., 2001: Coupling cloud processes with large-scale dynamics using the Cloud-Resolving Convection Parameterization (CRCP). J. Atmos. Sci., 58 , 978997.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., 2003: MJO-like coherent structures: Sensitivity simulations using the Cloud-Resolving Convection Parameterization (CRCP). J. Atmos. Sci., 60 , 847864.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., and M. W. Moncrieff, 2001: Large-scale organization of tropical convection in two dimensional explicit numerical simulations. Quart. J. Roy. Meteor. Soc., 127 , 445468.

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., J-I. Yano, and M. W. Moncrieff, 2000: Cloud-resolving modeling of tropical circulations driven by large-scale SST gradients. J. Atmos. Sci., 57 , 20222039.

    • Search Google Scholar
    • Export Citation
  • Haertel, P. T., and G. N. Kiladis, 2004: On the dynamics of two-day equatorial disturbances. J. Atmos. Sci., 61 , 27072721.

  • Johnson, R. H., T. M. Rickenbach, S. A. Rutledge, P. E. Ciesielski, and W. H. Schubert, 1999: Trimodal characteristics of tropical convection. J. Climate, 12 , 23972407.

    • Search Google Scholar
    • Export Citation
  • Khouider, B., and A. J. Majda, 2005a: A non-oscillatory well balanced scheme for an idealized tropical climate model. Part I: Algorithm and validation. Theor. Comp. Fluid. Dyn., 19 , 331354.

    • Search Google Scholar
    • Export Citation
  • Khouider, B., and A. J. Majda, 2005b: A non-oscillatory well balanced scheme for an idealized tropical climate model. Part II: Nonlinear coupling and moisture effects. Theor. Comp. Fluid Dyn., 19 , 355375.

    • Search Google Scholar
    • Export Citation
  • Khouider, B., and A. J. Majda, 2006a: A simple multicloud parameterization for convectively coupled tropical waves. Part I: Linear analysis. J. Atmos. Sci., 63 , 13181323.

    • Search Google Scholar
    • Export Citation
  • Khouider, B., and A. J. Majda, 2006b: Model multicloud parameterizations for convectively coupled waves: Detailed nonlinear wave evolution. Dyn. Atmos. Oceans, 42 , 5980.

    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., K. H. Straub, and P. Haertel, 2005: Zonal and vertical structure of the Madden–Julian oscillation. J. Atmos. Sci., 62 , 27902809.

    • Search Google Scholar
    • Export Citation
  • Lin, J-L., and B. Mapes, 2004: Wind shear effects on cloud-radiation feedback in the western Pacific warm pool. Geophys. Res. Lett., 31 .L16118, doi:10.1029/2004GL020199.

    • Search Google Scholar
    • Export Citation
  • Lin, X., and R. H. Johnson, 1996: Kinematic and thermodynamic characteristics of the flow over the Western Pacific Warm Pool during TOGA COARE. J. Atmos. Sci., 53 , 695715.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R. S., 1974: Wave–CISK in the Tropics. J. Atmos. Sci., 31 , 156179.

  • Majda, A. J., and M. Shefter, 2001: Models for stratiform instability and convectively coupled waves. J. Atmos. Sci., 58 , 15671584.

  • Majda, A. J., and B. Khouider, 2002: Stochastic and mesoscopic models for tropical convection. Proc. Natl. Acad. Sci. USA, 99 , 11231128.

    • Search Google Scholar
    • Export Citation
  • Majda, A. J., B. Khouider, G. N. Kiladis, K. H. Straub, and M. G. Shefter, 2004: A model for convectively coupled tropical waves: Nonlinearity, rotation, and comparison with observations. J. Atmos. Sci., 61 , 21882205.

    • Search Google Scholar
    • Export Citation
  • Mapes, B. E., 2000: Convective inhibition, subgrid-scale triggering energy, and “stratiform instability” in a toy tropical wave model. J. Atmos. Sci., 57 , 15151535.

    • Search Google Scholar
    • Export Citation
  • Moncrieff, M. W., and E. Klinker, 1997: Organized convective systems in the tropical western Pacific as a process in general circulation models: A TOGA-COARE case study. Quart. J. Roy. Meteor. Soc., 123 , 805827.

    • Search Google Scholar
    • Export Citation
  • Nakazawa, T., 1988: Tropical super clusters within intraseasonal variations over the western Pacific. J. Meteor. Soc. Japan, 66 , 823839.

    • Search Google Scholar
    • Export Citation
  • Neelin, J. D., and J. Yu, 1994: Modes of tropical variability under convective adjustment and Madden–Julian oscillation. Part I: Analytical theory. J. Atmos. Sci., 51 , 18761894.

    • Search Google Scholar
    • Export Citation
  • Neelin, J. D., and N. Zeng, 2000: A quasi-equilibrium tropical circulation model—Formulation. J. Atmos. Sci., 57 , 17411766.

  • Peters, M. E., and C. S. Bretherton, 2006: Structure of tropical variability from a vertical mode perspective. Theor. Comp. Fluid Dyn., 20 , 501524.

    • Search Google Scholar
    • Export Citation
  • Slingo, J. M., and Coauthors, 1996: Intraseasonal oscillation in 15 atmospheric general circulation models: Results from an AMIP diagnostic subproject. Climate Dyn., 12 , 325357.

    • Search Google Scholar
    • Export Citation
  • Sperber, K. R., J. M. Slingo, P. K. Inness, and W. K-M. Lau, 1997: On the maintenance and initiation of the intraseasonal oscillation in the NCEP/NCAR reanalysis and in the GLA and UKMO AMIP simulations. Climate Dyn., 13 , 769795.

    • Search Google Scholar
    • Export Citation
  • Straub, K. H., and G. N. Kiladis, 2002: Observations of a convectively-coupled Kelvin wave in the eastern Pacific ITCZ. J. Atmos. Sci., 59 , 3053.

    • Search Google Scholar
    • Export Citation
  • Tompkins, A. M., 2001a: Organization of tropical convection in low vertical wind shears: The role of water vapor. J. Atmos. Sci., 58 , 349364.

    • Search Google Scholar
    • Export Citation
  • Tompkins, A. M., 2001b: On the relationship between tropical convection and sea surface temperature. J. Climate, 14 , 633637.

  • Tulich, S. N., D. A. Randall, and B. E. Mapes, 2007: Vertical-mode and cloud decomposition of large-scale convectively coupled gravity waves in a two dimensional cloud-resolving model. J. Atmos. Sci., in press.

    • Search Google Scholar
    • Export Citation
  • Wheeler, M., and G. N. Kiladis, 1999: Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber-frequency domain. J. Atmos. Sci., 56 , 374399.

    • Search Google Scholar
    • Export Citation
  • Wheeler, M., G. N. Kiladis, and P. J. Webster, 2000: Large-scale dynamical fields associated with convectively coupled equatorial waves. J. Atmos. Sci., 57 , 613640.

    • Search Google Scholar
    • Export Citation
  • Yano, J-I., and K. A. Emanuel, 1991: An improved model of the equatorial troposphere and its coupling to the stratosphere. J. Atmos. Sci., 48 , 377389.

    • Search Google Scholar
    • Export Citation
  • Yano, J-I., J. C. McWilliams, M. W. Moncrieff, and K. A. Emanuel, 1995: Hierarchical tropical cloud systems in an analog shallow-water model. J. Atmos. Sci., 52 , 17231742.

    • Search Google Scholar
    • Export Citation
  • Zehnder, J. A., 2001: A comparison of convergence- and surface-flux-based convective parameterizations with applications to tropical cyclogenesis. J. Atmos. Sci., 58 , 283301.

    • Search Google Scholar
    • Export Citation
  • Zhang, C., 2005: Madden-Julian Oscillation. Rev. Geophys., 43 .RG2003, doi:10.1029/2004RG000158.

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