A skeleton model for the MJO with refined vertical structure

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 dω/ dk≈ 0 , and (III) a horizontal quadrupole vortex structure. This 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 propose and analyse an extended version of the skeleton model with additional variables accounting for the refined vertical structure of the MJO in nature. The present model reproduces qualitatively the front-to-rear vertical structure of the MJO found in nature, with MJO events marked by a planetary envelope of convective activity transitioning from the congestus to the deep to the stratiform type, in addition to a front-to-rear structure of moisture, winds and temperature. Despite its increased complexity the present model retains several interesting features of the original skeleton model such as a conserved energy and similar linear solutions. We further analyze a model version with a simple stochastic parametrization for the unresolved details of synoptic-scale activity. The stochastic model solutions show intermittent initiation, propagation and shut down of MJO wave trains, as in previous studies, in addition to MJO events with a front-to-rear vertical structure of varying intensity and characteristics from one event to another.