Nonlinear dynamics and regional variations in the MJO skeleton

Andrew J. Majda, Samuel N. Stechmann

Research output: Contribution to journalArticlepeer-review


A minimal, nonlinear oscillator model is analyzed for the Madden-Julian oscillation (MJO) "skeleton" (i.e., its fundamental features on intraseasonal/planetary scales), which includes the following: (i) a slow eastward phase speed of roughly 5 m s -1, (ii) a peculiar dispersion relation with dω/dk ≈ 0, and (iii) a horizontal quadrupole vortex structure. Originally proposed in recent work by the authors, the fundamental mechanism involves neutrally stable interactions between (i) planetary-scale, lower-tropospheric moisture anomalies and (ii) the envelope of subplanetary-scale, convection/wave activity. Here, the model's nonlinear dynamics are analyzed in a series of numerical experiments, using either a uniform sea surface temperature (SST) or a warm-pool SST. With a uniform SST, the results show significant variations in the number, strength, and/or locations of MJO events, including, for example, cases of a strong MJO event followed by a weaker MJO event, similar to the Tropical Ocean and Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE). With a warm-pool SST, MJO events often begin as standing oscillations and then propagate slowly eastward across the warm pool, a behavior imitating MJOs in nature. While displaying the fundamental features of the MJO skeleton, these MJO events had significant variations in their lifetimes and regional extents, and they displayed intense, irregular fluctuations in their amplitudes. The model reproduces all of these features of the MJO skeleton without including mechanisms for the MJO's "muscle," such as refined vertical structure and upscale convective momentum transport from subplanetaryscale convection/waves. Besides these numerical experiments, it is also shown that the nonlinear model conserves a total energy that includes a contribution from the convective activity.

Original languageEnglish (US)
Pages (from-to)3053-3071
Number of pages19
JournalJournal of the Atmospheric Sciences
Issue number12
StatePublished - Dec 2011


  • Intraseasonal variability
  • Madden-Julian oscillation
  • Nonlinear models
  • Tropical variabilty

ASJC Scopus subject areas

  • Atmospheric Science


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