EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

The dynamical composition of the Madden-Julian oscillation

José M. Castanheira and Carlos A. F. Marques
José M. Castanheira and Carlos A. F. Marques
  • CESAM & Departamento de Física, Universidade de Aveiro, Aveiro, Portugal (

The Madden-Julian oscillation (MJO) is a major intraseasonal tropical atmospheric mode which modulates the precipitation in the Tropical Indian and Pacific  oceans. It is a large atmospheric convective system, dominated the zonal wave number one scale, that moves eastward from the east coast of Africa to eastern Pacific in a time scale of  30-70 days.

The MJO can have impact in global weather but is yet poorly simulated in most atmospheric circulation models. Therefore, it is important to understand the convective-dynamical nature of the MJO to understand the reasons for its poor representation in models.

Here we present a diagnostic study of the MJO by decomposing the circulation associated with a multivariate MJO index onto 3-Dimensional inertio-gravitic and Rossby modes, based on the ERA-I reanalysis. Results show that the main dynamical features of MJO are represented by  a combination of  Kelvin and the first (lr = 1) equatorial Rossby modes with zonal wavenumbers 1 to 4. The vertical structures of the waves correspond to a first baroclinic mode in the troposphere. Moreover, a space–time spectral analysis confirmed the existence of an eastward moving MJO signal in the equatorial Rossby modes.

Nonlinear interactions between the westward moving equatorial Rossby waves and eastward moving Kelvin waves may be the cause for the slow eastward progression of the MJO. 

How to cite: Castanheira, J. M. and Marques, C. A. F.: The dynamical composition of the Madden-Julian oscillation, EGU General Assembly 2020, Online, 4–8 May 2020,, 2020

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Presentation version 3 – uploaded on 18 May 2020 , no comments
Correction of unities in the two first Figures.
Presentation version 2 – uploaded on 05 May 2020
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  • CC1: Comment on EGU2020-19806, Paul Pukite, 06 May 2020

    "yet poorly simulated in most atmospheric circulation models"

    Is that because it's not well known that it is connected directly to ENSO via the SOI measure with a 21-day lag?

    and ENSO is difficult to model

    • AC3: Reply to CC1, José M. Castanheira, 06 May 2020

      What index do you use for the MJO?
      Did you try to calculate the correlation with the interannual variability removed?

      • CC4: Reply to AC3, Paul Pukite, 06 May 2020

        From NOAA, the high-resolution (pentad=5-day) time-series of MJO

        This matches to SOI both with inter-annual and much of the intra-annual after a 21-day shift


      • AC4: Reply to AC3, José M. Castanheira, 06 May 2020

        Please see my comment AC1.

  • CC2: Comment on EGU2020-19806, Guosen Chen, 06 May 2020

    What's the energy source for the Rossby wave?

    • CC3: Reply to CC2, Paul Pukite, 06 May 2020

      If I may insert my learned opinion, I think the source of the energy for the Rossby waves is tidal forcing, along with the Coriolis effect.  There's a way to solve Laplace's Tidal (primitive GCM) Equations along the equator (where the Coriolis cancels) so that the standing waves of ENSO are readily revealed. The Madden-Julian Oscillations are the travelling-wave offshoots.

      see also:

      Lin, J. & Qian, T. Switch Between El Nino and La Nina is Caused by Subsurface Ocean Waves Likely Driven by Lunar Tidal Forcing. Sci Rep 9, 1–10 (2019).
    • AC2: Reply to CC2, José M. Castanheira, 06 May 2020

      Thank you for your question.

      Please see my author comment AC1.

  • AC1: Comment on EGU2020-19806, José M. Castanheira, 06 May 2020

    In think the energy source for Rossby waves is the organized convection trough atmospheric column stretching. Citing Geoffrey K. Vallis (pag. 326, 2017) ''From the perspective of potential vorticity, then to the extent that the flow is adiabatic the quantity (𝑓 + 𝜁)/ℎ is conserved following the flow. The heating increases the value of ℎ (the stretching), so that 𝑓 + 𝜁 also tends to increase in magnitude. The flow finds it easier to migrate polewards to increase its value of 𝑓 than to increase its relative vorticity alone, for the latter would require more energy.'' Then a pair of cyclonic centers is formed straddling the equator.

Presentation version 1 – uploaded on 05 May 2020 , no comments