A Suite of Skeleton Models for the MJO with
Refined Vertical Structure

• Authors: Sulian Thual , Andrew J. Majda
• Languages of publication: EN

Abstracts

EN

The Madden-Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere
on intraseasonal timescales and planetary spatial scales. The skeleton model is a minimal dynamical model
that recovers robustly the most fundamental MJO features of (I) a slow eastward speed of roughly 5 ms−1, (II)
a peculiar dispersion relation with dw/dk ≈ 0, and (III) a horizontal quadrupole vortex structure. This model
depicts the MJO as a neutrally-stable atmosphericwave that involves a simple multiscale interaction between
planetary dry dynamics, planetary lower-tropospheric moisture and the planetary envelope of synoptic-scale
activity. Here we propose and analyze a suite of skeleton models that qualitatively reproduce the refined vertical
structure of the MJO in nature. This vertical structure consists of a planetary envelope of convective activity
transitioning from the congestus to the deep to the stratiform type, in addition to a front-to-rear (i.e. tilted)
structure of heating, moisture, winds and temperature. A first example of skeleton model achieving this goal
has been considered recently in work by the authors. The construction of such a model satisfies an energy
conservation principle, such that its solutions at the intraseasonal-planetary scale remain neutrally stable.
Here, additional classes of skeleton models are constructed based on the same principle. In particular, those
new models are more realistic then the former one as they consider fully coupled interactions between the
planetary dry dynamics of the first and second baroclinic mode and the details of the vertical structure of
moisture and convective activity. All models reproduce qualitatively the refined vertical structure of the MJO.
In addition,when considered with a simple stochastic parametrization for the unresolved details of synopticscale
activity, all models show intermittent initiation, propagation and shut down of MJO wave trains, as in
previous studies.

• Publisher: De Gruyter Open
• Journal: Mathematics of Climate and Weather Forecasting
• Year: 2015
• Volume: 1
• Issue: 1

Dates

accepted

27 - 10 - 2015

online

30 - 11 - 2015

received

6 - 8 - 2015

Contributors

author

Sulian Thual

• Department of Mathematics, and Center for Atmosphere Ocean Science,
  Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 USA

author

Andrew J. Majda

• Department of Mathematics, and Center for Atmosphere Ocean Science, Courant Institute of Mathematical
  Sciences, New York University, 251 Mercer Street, New York, NY 10012 USA

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Identifiers

DOI

10.1515/mcwf-2015-0004