A Stochastic Skeleton Model for the MJO

Abstract:

The Madden–Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on

intraseasonal time scales and planetary spatial scales. Despite the primary importance of the MJO and the

decades of research progress since its original discovery, a generally accepted theory for its essential mechanisms

has remained elusive. In recent work by two of the authors, a minimal dynamical model has been

proposed that recovers robustly the most fundamental MJO features of (i) a slow eastward speed of roughly

5 m/s, (ii) a peculiar dispersion relation with dω/dk≈0, and (iii) a horizontal quadrupole vortex structure.

This model, the skeleton model, depicts the MJO as a neutrally stable atmospheric wave that involves a simple

multiscale interaction between planetary dry dynamics, planetary lower-tropospheric moisture, and the

planetary envelope of synoptic-scale activity. In this article, it is shown that the skeleton model can further

account for (iv) the intermittent generation of MJO events and (v) the organization of MJO events into wave

trains with growth and demise, as seen in nature. The goal is achieved by developing a simple stochastic

parameterization for the unresolved details of synoptic-scale activity, which is coupled to otherwise deterministic

processes in the skeleton model. In particular, the intermittent initiation, propagation, and shut

down of MJO wave trains in the skeleton model occur through these stochastic effects. This includes examples

with a background warm pool where some initial MJO-like disturbances propagate through the western region

but stall at the peak of background convection/heating corresponding to the Maritime Continent in nature. Also shown are examples with an idealized seasonal cycle, namely a background warm pool state of heating/moistening displacing meridionally during the year. This seasonally varying case considers both equatorial and off-equatorial components of the envelope of synoptic scale convective activity, which allows for a large diversity of meridionally symmetric and asymmetric intraseasonal events found in nature.