A coupled moisture-dynamics model of the Madden–Julian oscillation: convection interaction with first and second baroclinic modes and planetary boundary layer

Abstract

A theoretical model with a single prognostic variable, column-integrated moist static energy (MSE), was constructed to understand the dynamics of MJO eastward propagation and planetary scale selection. A key process in the model is the interaction of MSE-dependent convection with free-atmospheric first, second baroclinic modes and planetary boundary layer. Under a realistic parameter regime, the model reproduces the most unstable mode at zonal wavenumber 1 with a slow eastward phase speed of about 5 ms−1. The slow eastward phase speed in the model arises from the competition of eastward moving MSE tendencies caused by horizontal MSE advection, vertical MSE advection and boundary layer moistening with westward moving tendencies contributed by surface latent heat flux and atmospheric longwave radiative heating. The planetary scale selection is primarily attributed to the phase lag of longwave radiative heating associated with upper-level stratiform clouds that occur in the rear of MJO deep convection.