A Stochastic Skeleton Model for the MJO

The Madden-Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on intraseasonal timescales and planetary spatial scales. 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 ms-1, (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.

Here, we show 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. We achieve this goal by developing a simple stochastic parametrization for the unresolved details of synoptic-scale activity, that 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.