Kinetic Energy Budget for the Madden–Julian Oscillation in a Multiscale Framework

Lei Zhou Lamont-Doherty Earth Observatory, Columbia University, New York, New York, and State Key Lab of Satellite Ocean Environment Dynamics, SIO, SOA, Hangzhou, China

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Adam H. Sobel Department of Applied Physics and Applied Mathematics, and Department of Earth and Environmental Sciences, and Lamont-Doherty Earth Observatory, Columbia University, New York, New York

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Raghu Murtugudde Earth System Science Interdisciplinary Center, University of Maryland, College Park, College, Park, Maryland

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Abstract

A kinetic energy budget for the Madden–Julian oscillation (MJO) is established in a three-scale framework. The three scales are the zonal mean, the MJO scale with wavenumbers 1–4, and the small scale with wavenumbers larger than 4. In the composite budget, the dominant balance at the MJO scale is between conversion from potential energy and work done by the pressure gradient force (PGF). This balance is consistent with the view that the MJO wind perturbations can be viewed as a quasi-linear response to a slowly varying heat source. A large residual in the upper troposphere suggests that much kinetic energy dissipates there by cumulus friction. Kinetic energy exchange between different scales is not a large component of the composite budget. There is a transfer of kinetic energy from the MJO scale to the small scale; that is, this multiscale interaction appears to damp rather than strengthen the MJO. There is some variation in the relative importance of different terms from one event to the next. In particular, conversion from mean kinetic energy can be important in some events. In a few other events, the influence from the extratropics is pronounced.

Corresponding author address: Lei Zhou, 301d Oceanography, Lamont-Doherty Earth Observatory, 61 Route 9W, Palisades, NY 10964. E-mail: lzhou@ldeo.columbia.edu

Abstract

A kinetic energy budget for the Madden–Julian oscillation (MJO) is established in a three-scale framework. The three scales are the zonal mean, the MJO scale with wavenumbers 1–4, and the small scale with wavenumbers larger than 4. In the composite budget, the dominant balance at the MJO scale is between conversion from potential energy and work done by the pressure gradient force (PGF). This balance is consistent with the view that the MJO wind perturbations can be viewed as a quasi-linear response to a slowly varying heat source. A large residual in the upper troposphere suggests that much kinetic energy dissipates there by cumulus friction. Kinetic energy exchange between different scales is not a large component of the composite budget. There is a transfer of kinetic energy from the MJO scale to the small scale; that is, this multiscale interaction appears to damp rather than strengthen the MJO. There is some variation in the relative importance of different terms from one event to the next. In particular, conversion from mean kinetic energy can be important in some events. In a few other events, the influence from the extratropics is pronounced.

Corresponding author address: Lei Zhou, 301d Oceanography, Lamont-Doherty Earth Observatory, 61 Route 9W, Palisades, NY 10964. E-mail: lzhou@ldeo.columbia.edu
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  • Biello, J. A., and A. J. Majda, 2005: A new multiscale model for the Madden–Julian oscillation. J. Atmos. Sci., 62, 16941721.

  • Biello, J. A., A. J. Majda, and M. W. Moncrieff, 2007: Meridional momentum flux and superrotation in the multiscale IPESD MJO model. J. Atmos. Sci., 64, 16361651.

    • Search Google Scholar
    • Export Citation
  • Blade, I., and D. L. Hartmann, 1993: Tropical intraseasonal oscillations in a simple nonlinear model. J. Atmos. Sci., 50, 29222939.

  • Bretherton, C. S., and A. H. Sobel, 2003: The Gill model and the weak temperature gradient approximation. J. Atmos. Sci., 60, 451460.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1987: An air–sea interaction model of intraseasonal oscillations in the tropics. J. Atmos. Sci., 44, 23242340.

  • Ferreira, R. N., and W. H. Schubert, 1997: Barotropic aspects of ITCZ breakdown. J. Atmos. Sci., 54, 261285.

  • Gill, A. E., 1980: Some simple solutions for heat-induced tropical circulation. Quart. J. Roy. Meteor. Soc., 106, 447462.

  • Hendon, H. H., and M. L. Salby, 1994: The life cycle of the Madden–Julian oscillation. J. Atmos. Sci., 51, 22252237.

  • Holton, J. R., 2004: An Introduction to Dynamic Meteorology. 4th ed. Academic Press, 535 pp.

  • Houze, R. A., Jr., 1982: Cloud clusters and large-scale vertical motions in the tropics. J. Meteor. Soc. Japan, 60, 396409.

  • Hsu, H.-H., B. J. Hoskins, and F.-F. Jin, 1990: The 1985/86 intraseasonal oscillation and the role of the extratropics. J. Atmos. Sci., 47, 823839.

    • Search Google Scholar
    • Export Citation
  • Hu, Q., and D. A. Randall, 1995: Low-frequency oscillations in radiative convective systems 2. An idealized model. J. Atmos. Sci., 52, 478490.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437471.

  • Kemball-Cook, S. R., and B. C. Weare, 2001: The onset of convection in the Madden–Julian oscillation. J. Climate, 14, 780793.

  • Kiladis, G. N., M. C. Wheeler, P. T. Haertel, K. H. Straub, and P. E. Roundy, 2009: Convectively coupled equatorial waves. Rev. Geophys., 47, RG2003, doi:10.1029/2008RG000266.

    • Search Google Scholar
    • Export Citation
  • Lau, K.-H., and N.-C. Lau, 1992: The energetics and propagation dynamics of tropical summertime synoptic-scale disturbances. Mon. Wea. Rev., 120, 25232539.

    • Search Google Scholar
    • Export Citation
  • Lau, K. M., and L. Peng, 1987: Origin of low-frequency (intraseasonal) oscillations in the tropical atmosphere 1. Basic theory. J. Atmos. Sci., 44, 950972.

    • Search Google Scholar
    • Export Citation
  • Leith, C. E., 1973: The standard error of time-average estimates of climatic means. J. Appl. Meteor., 12, 10661069.

  • Lin, H., G. Brunet, and J. Derome, 2007: Intraseasonal variability in a dry atmospheric model. J. Atmos. Sci., 64, 24222441.

  • Lin, J. L., M. H. Zhang, and B. Mapes, 2005: Zonal momentum budget of the Madden–Julian oscillation: The source and strength of equivalent linear damping. J. Atmos. Sci., 62, 21722188.

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

  • Lorenz, E. N., 1955: Available potential energy and the maintenance of the general circulation. Tellus, 7, 157167.

  • Madden, R. A., and P. R. Julian, 1971: Detection of a 40–50-day oscillation in zonal wind in tropical Pacific. J. Atmos. Sci., 28, 702708.

    • Search Google Scholar
    • Export Citation
  • Madden, R. A., and P. R. Julian, 1972: Description of global-scale circulation cells in tropics with a 40–50-day period. J. Atmos. Sci., 29, 11091123.

    • Search Google Scholar
    • Export Citation
  • Madden, R. A., and P. R. Julian, 1994: Observations of the 40–50-day tropical oscillation—A review. Mon. Wea. Rev., 122, 814837.

  • Majda, A. J., 2007a: New multiscale models and self-similarity in tropical convection. J. Atmos. Sci., 64, 13931404.

  • Majda, A. J., 2007b: Multiscale models with moisture and systematic strategies for superparameterization. J. Atmos. Sci., 64, 27262734.

    • Search Google Scholar
    • Export Citation
  • Maloney, E. D., and D. L. Hartmann, 2001: The Madden–Julian oscillation, barotropic dynamics, and North Pacific tropical cyclone formation. Part I: Observations. J. Atmos. Sci., 58, 25452558.

    • Search Google Scholar
    • Export Citation
  • Maloney, E. D., and M. J. Dickinson, 2003: The intraseasonal oscillation and the energetics of summertime tropical western North Pacific synoptic-scale disturbances. J. Atmos. Sci., 60, 21532168.

    • Search Google Scholar
    • Export Citation
  • Matthews, A. J., 2008: Primary and successive events in the Madden–Julian oscillation. Quart. J. Roy. Meteor. Soc., 134, 439453.

  • Matthews, A. J., and G. N. Kiladis, 1999: The tropical–extratropical interaction between high-frequency transients and the Madden–Julian oscillation. Mon. Wea. Rev., 127, 661677.

    • Search Google Scholar
    • Export Citation
  • Milliff, R. F., J. Morzel, D. B. Chelton, and M. H. Freilich, 2004: Wind stress curl and wind stress divergence biases from rain effects on QSCAT surface wind retrievals. J. Atmos. Oceanic Technol., 21, 12161231.

    • Search Google Scholar
    • Export Citation
  • Miyakawa, T., Y. N. Takayabu, T. Nasuno, H. Miura, M. Satoh, and M. Moncrieff, 2012: Convective momentum transport by rainbands within a Madden–Julian oscillation in a global nonhydrostatic model with explicit deep convective processes. Part I: Methodology and general results. J. Atmos. Sci., 69, 13171338.

    • Search Google Scholar
    • Export Citation
  • Moncrieff, M. W., 2004: Analytic representation of the large-scale organization of tropical convection. J. Atmos. Sci., 61, 15211538.

    • Search Google Scholar
    • Export Citation
  • Neelin, J. D., I. M. Held, and K. H. Cook, 1987: Evaporation–wind feedback and low-frequency variability in the tropical atmosphere. J. Atmos. Sci., 44, 23412348.

    • Search Google Scholar
    • Export Citation
  • Nitta, T., 1972: Energy budget of wave disturbances over the Marshall Islands during the years of 1956 and 1958. J. Meteor. Soc. Japan, 50, 7184.

    • Search Google Scholar
    • Export Citation
  • Nitta, T., and M. Yanai, 1969: A note on the barotropic instability of the tropical easterly current. J. Meteor. Soc. Japan, 47, 127130.

    • Search Google Scholar
    • Export Citation
  • Ray, P., and C. D. Zhang, 2010: A case study of the mechanics of extratropical influence on the initiation of the Madden–Julian oscillation. J. Atmos. Sci., 67, 515528.

    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., 2001: A new model of the Madden–Julian oscillation. J. Atmos. Sci., 58, 28072819.

  • Schumacher, C., R. A. Houze, and I. Kraucunas, 2004: The tropical dynamical response to latent heating estimates derived from the TRMM precipitation radar. J. Atmos. Sci., 61, 13411358.

    • Search Google Scholar
    • Export Citation
  • Seiki, A., and Y. N. Takayabu, 2007: Westerly wind bursts and their relationship with intraseasonal variations and ENSO. Part II: Energetics over the western and central pacific. Mon. Wea. Rev., 135, 33463361.

    • Search Google Scholar
    • Export Citation
  • Slingo, J. M., P. M. Inness, and K. R. Sperber, 2005: Modeling. Intraseasonal Variability in the Atmosphere-Ocean Climate System, W. K. M. Lau and D. Waliser, Eds., Springer-Praxis, 361–388.

  • Sobel, A. H., and C. S. Bretherton, 1999: Development of synoptic-scale disturbances over the summertime tropical northwest Pacific. J. Atmos. Sci., 56, 31063127.

    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., and H. Gildor, 2003: A simple time-dependent model of SST hot spots. J. Climate, 16, 39783992.

  • Sobel, A. H., and E. D. Maloney, 2012: An idealized semi-empirical framework for modeling the Madden-Julian oscillation. J. Atmos. Sci., 69, 16911705.

    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., E. D. Maloney, G. Bellon, and D. M. Frierson, 2008: The role of surface heat fluxes in tropical intraseasonal oscillations. Nat. Geosci., 1, 653657.

    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., E. D. Maloney, G. Bellon, and D. M. Frierson, 2010: Surface fluxes and tropical intraseasonal variability: A reassessment. J. Adv. Model Earth Syst., 2, doi:10.3894/JAMES.2010.2.2.

    • Search Google Scholar
    • Export Citation
  • Sugiyama, M., 2009: The moisture mode in the quasi-equilibrium tropical circulation model. Part I: Analysis based on the weak temperature gradient approximation. J. Atmos. Sci., 66, 15071523.

    • Search Google Scholar
    • Export Citation
  • Taylor, G. I., 1921: Diffusion by continuous movement. Proc. London Math. Soc., 21, 196212.

  • Tung, W. W., and M. Yanai, 2002: Convective momentum transport observed during the TOGA COARE IOP. Part I: General features. J. Atmos. Sci., 59, 18571871.

    • Search Google Scholar
    • Export Citation
  • Uppala, S. M., and Coauthors, 2005: The ERA-40 Re-Analysis. Quart. J. Roy. Meteor. Soc., 131, 29613012.

  • Wang, B., 2005: Theory. Intraseasonal Variability in the Atmosphere-Ocean Climate System, W. K. M. Lau and D. Waliser, Eds., Springer-Praxis, 307–360.

  • Wang, B., and H. Rui, 1990: Synoptic climatology of transient tropical intraseasonal convection anomalies—1975–1985. Meteor. Atmos. Phys., 44, 4361.

    • Search Google Scholar
    • Export Citation
  • Wang, C.-C., and G. Magnusdottir, 2006: The ITCZ in the central and eastern Pacific on synoptic time scales. Mon. Wea. Rev., 134, 14051421.

    • Search Google Scholar
    • Export Citation
  • Webster, P. J., and H.-R. Chang, 1988: Equatorial energy accumulation and emanation regions: Impacts of a zonally varying basic state. J. Atmos. Sci., 45, 803829.

    • Search Google Scholar
    • Export Citation
  • Weickmann, K., and E. Berry, 2009: The tropical Madden–Julian oscillation and the global wind oscillation. Mon. Wea. Rev., 137, 16011614.

    • Search Google Scholar
    • Export Citation
  • Wheeler, M. C., and H. H. Hendon, 2004: An all-season real-time multivariate MJO index: Development of an index for monitoring and prediction. Mon. Wea. Rev., 132, 19171932.

    • Search Google Scholar
    • Export Citation
  • Yanai, M., B. Chen, and W. W. Tung, 2000: The Madden–Julian oscillation observed during the TOGA COARE IOP: Global view. J. Atmos. Sci., 57, 23742396.

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

  • Zhou, L., R. Neale, M. Jochum, and R. Murtugudde, 2012: Improved Madden–Julian oscillations with improved physics: The impact of modified convection parameterizations. J. Climate, 25, 11161136.

    • Search Google Scholar
    • Export Citation
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