Climate Dynamics

, Volume 40, Issue 1–2, pp 213–224 | Cite as

Impacts of upscale heat and momentum transfer by moist Kelvin waves on the Madden–Julian oscillation: a theoretical model study

  • Fei Liu
  • Bin WangEmail author


The Madden–Julian oscillation (MJO) is observed to interact with moist Kelvin waves. To understand the role of this interaction, a simple scale-interaction model is built, which describes the MJO modulation of moist Kelvin waves and the feedback from moist Kelvin waves through upscale eddy heat and momentum transfer. The backward-tilted moist Kelvin waves produce eddy momentum transfer (EMT) characterized by the lower-tropospheric westerly winds and eddy heat transfer (EHT) that warms the mid-troposphere. The EHT tends to induce the lower-tropospheric easterly winds and low pressure, which is located in front of the “westerly wind burst” induced by the EMT. Adding the eddy forcing to a neutral MJO skeleton model, we show that the EHT provides an instability source for the MJO by warming up the mid-troposphere, and the EMT offers an additional instability source by enhancing the lower-tropospheric westerly winds. The eddy forcing selects eastward propagation for the unstable mode, because it generates positive/negative eddy available potential energy for the eastward/westward modes by changing their thermal and dynamical structures. The present results show that moist Kelvin waves can provide a positive feedback to the MJO only when they are located within (or near) the convective complex (center) of the MJO. The EHT and EMT feedback works positively in the front and rear part of the MJO, respectively. These theoretical results suggest the potential importance of moist Kelvin waves in sustaining the MJO and encourage further observations to document the relationship between moist Kelvin waves and the MJO.


Madden–Julian oscillation Moist Kelvin waves Scale interaction Eddy heat transfer Eddy momentum transfer 



The authors thank two anonymous reviews for their comments and suggestions. This study was supported by Climate Dynamics Program of the National Science Foundation under award No AGS-1005599 and Global Research Laboratory (GRL) Program from the Ministry of Education, Science, and Technology (MEST), Korea. Additional support was provided by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC), by NASA through grant NNX07AG53G, and by NOAA through grant NA17RJ1230 through their sponsorship of research activities at the International Pacific Research Center. This paper is the SOEST Contribution No. 8551 and IPRC publication No. 839.


  1. Biello JA, Majda AJ (2005) A new multiscale model for the Madden–Julian oscillation. J Atmos Sci 62:1694–1721CrossRefGoogle Scholar
  2. Biello JA, Majda AJ (2006) Modulating synoptic scale convective activity and boundary layer dissipation in the IPESD models of the Madden-Julian oscillation. Dyn Atmos Oceans 42:152–215CrossRefGoogle Scholar
  3. Frierson D, Majda AJ, Pauluis O (2004) Dynamics of precipitation fronts in the tropical atmosphere. Comm Math Sci 2:591–626Google Scholar
  4. Gill AE (1980) Some simple solutions for heat-induced tropical circulation. Q J R Meteor Soc 106:447–462CrossRefGoogle Scholar
  5. Haertel PT, Kiladis GN (2004) Dynamics of 2-Day equatorial waves. J Atmos Sci 61:2707–2721CrossRefGoogle Scholar
  6. Houze RA Jr, Chen SS, Kingsmill DE, Serra Y, Yuter SE (2000) Convection over the Pacific warm pool in relation to the atmospheric Kelvin–Rossby wave. J Atmos Sci 57:3058–3089CrossRefGoogle Scholar
  7. Khouider B, Majda AJ (2006) A simple multicloud parameterization for convectively coupled tropical waves. Part I: linear analysis. J Atmos Sci 63:1308–1323CrossRefGoogle Scholar
  8. Khouider B, Majda AJ (2007) A simple multicloud parameterization for convectively coupled tropical waves. Part II. Nonlinear simulations. J Atmos Sci 64:381–400CrossRefGoogle Scholar
  9. Kikuchi K, Takayabu YN (2004) The development of organized convection associated with the MJO during TOGA COARE IOP: trimodal characteristics. Geophys Res Lett 31:L10101. doi: 10.1029/2004GL019601 CrossRefGoogle Scholar
  10. Kikuchi K, Wang B (2010) Spatiotemporal wavelet transform and the multiscale behavior of the Madden–Julian oscillation. J Clim 23:3814–3834CrossRefGoogle Scholar
  11. Kiladis GN, Straub KH, Haertel PT (2005) Zonal and vertical structure of the Madden–Julian oscillation. J Atmos Sci 62:2790–2809CrossRefGoogle Scholar
  12. Kiladis GN, Wheeler MC, Haertel PY, Straub KH, Roundy PE (2009) Convectively coupled equatorial waves. Rev Geophys 47:RG2003Google Scholar
  13. Lin X, Johnson RH (1996) Kinematic and thermodynamic characteristics of the flow over the western Pacific warm pool during TOGA COARE. J Atmos Sci 53:695–715CrossRefGoogle Scholar
  14. Liu F, Wang B (2011) A model for the interaction between the 2-day waves and moist Kelvin waves. J Atmos Sci. doi: 10.1175/JAS-D-11-0116.1
  15. Liu F, Huang G, Feng L (2011) Critical roles of convective momentum transfer in sustaining the multi-scale Madden-Julian oscillation. Theor Appl Climatol. doi: 10.1007/s00704-011-0541-6
  16. Madden R, Julian P (1971) Detection of a 40–50 day oscillation in the zonal wind in the tropical Pacific. J Atmos Sci 28:702–708CrossRefGoogle Scholar
  17. Madden R, Julian P (1972) Description of global-scale circulation cells in the tropics with a 40–50 day period. J Atmos Sci 29:1109–1123CrossRefGoogle Scholar
  18. Madden R, Julian P (1994) Observations of the 40–50-day tropical oscillation—a review. Mon Weather Rev 122:814–837CrossRefGoogle Scholar
  19. Majda AJ (2003) Waves and PDEs for the equatorial atmosphere and ocean. Introduction to PDEs and waves for the Atmosphere and Ocean, Courant Institute Lecture Series 9. American Mathematical Society, pp 199–232Google Scholar
  20. Majda AJ, Biello JA (2004) A multiscale model for the intraseasonal oscillation. Proc Natl Acad Sci USA 101:4736–4741CrossRefGoogle Scholar
  21. Majda AJ, Klein R (2003) Systematic multiscale models for the tropics. J Atmos Sci 60:393–408CrossRefGoogle Scholar
  22. Majda AJ, Stechmann SN (2009a) A simple dynamical model with features of convective momentum transport. J Atmos Sci 66:373–392CrossRefGoogle Scholar
  23. Majda AJ, Stechmann SN (2009b) The skeleton of tropical intraseasonal oscillations. Proc Natl Acad Sci USA 106:8417–8422CrossRefGoogle Scholar
  24. Mapes BE (2000) Convective inhibition, subgrid-scale triggering energy, and stratiform instability in a toy tropical wave model. J Atmos Sci 57:1515–1535CrossRefGoogle Scholar
  25. Matsuno T (1966) Quasi-geostrophic motions in the equatorial area. J Meteorol Soc Jpn 44:25–43Google Scholar
  26. Moncrieff MW (2004) Analytic representation of the large-scale organization of tropical convection. J Atmos Sci 61:1521–1538CrossRefGoogle Scholar
  27. Moncrieff MW, 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 R Meteor Soc 123:805–827CrossRefGoogle Scholar
  28. Myers D, Waliser D (2003) Three-dimensional water vapor and cloud variations associated with the Madden–Julian oscillation during Northern Hemisphere winter. J Clim 16:929–950CrossRefGoogle Scholar
  29. Nakazawa T (1988) Tropical super clusters within intraseasonal variations over the western Pacific. J Meteor Soc Jpn 66:823–836Google Scholar
  30. Roundy PE (2008) Analysis of convectively coupled Kelvin waves in the Indian Ocean MJO. J Atmos Sci 65:1342–1359CrossRefGoogle Scholar
  31. Rui H, Wang B (1990) Development characteristics and dynamic structure of tropical intraseasonal convection anomalies. J Atmos Sci 47:357–379CrossRefGoogle Scholar
  32. Straub KH, Kiladis GN (2003) Interactions between the boreal summer intraseasonal oscillation and higher-frequency tropical wave activity. Mon Weather Rev 131:945–960CrossRefGoogle Scholar
  33. Takayabu YN, Murakami M (1991) The structure of super cloud clusters observed in 1–20 June 1986 and their relationship to easterly waves. J Meteor Soc Jpn 69:105–125Google Scholar
  34. Tian B, Waliser D, Fetzer E, Lambrigtsen B, Yung Y, Wang B (2006) Vertical moist thermodynamic structure and spatial–temporal evolution of the MJO in AIRS observations. J Atmos Sci 63:2462–2485CrossRefGoogle Scholar
  35. Waite ML, Khouider B (2009) Boundary layer dynamics in a simple model for convectively coupled gravity waves. J Atmos Sci 66:2780–2795CrossRefGoogle Scholar
  36. Wang B (1988) Dynamics of tropical low-frequency waves: an analysis of the moist Kelvin wave. J Atmos Sci 45:2051–2065CrossRefGoogle Scholar
  37. Wang B, Liu F (2011) A model for scale interaction in the Madden-Julian oscillation. J Atmos Sci. doi: 10.1175/2011JAS3660.1
  38. Wang B, Rui H (1990) Dynamics of coupled moist Kelvin-Rossby waves on an equatorial beta-plane. J Atmos Sci 47:397–413CrossRefGoogle Scholar
  39. Wang B, Xie X (1998) Coupled modes of the warm pool climate system. Part I: the role of air-sea interaction in maintaining Madden–Julian oscillation. J Clim 11:2116–2135CrossRefGoogle Scholar
  40. Wheeler M, Kiladis GN (1999) Convectively coupled equatorial waves: analysis of clouds and temperature in the wavenumber-frequency domain. J Atmos Sci 56:374–399CrossRefGoogle Scholar
  41. Yanai M, Chen B, Tung WW (2000) The Madden–Julian oscillation observed during the TOGA COARE IOP: global view. J Atmos Sci 57:2374–2396CrossRefGoogle Scholar
  42. Yano JI, Emanuel KA (1991) An improved model of the equatorial troposphere and its coupling to the stratosphere. J Atmos Sci 48:377–389CrossRefGoogle Scholar
  43. Zhang C (2005) Madden-Julian oscillation. Rev Geophys 43:RG2003. doi: 10.1029/2004RG000158

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.International Pacific Research CenterUniversity of Hawaii at ManoaHonoluluUSA
  2. 2.Department of MeteorologyUniversity of Hawaii at ManoaHonoluluUSA

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