A Frictional Skeleton Model for the Madden–Julian Oscillation*

Abstract

Abstract The Madden–Julian oscillation (MJO) is a multiscale system. A skeleton model, developed by Majda and Stechmann, can capture some of planetary-scale aspects of observed features such as slow eastward propagation, nondispersive behavior, and quadrupole-vortex structure. However, the Majda–Stechmann model cannot explain the source of instability and the preferred planetary scale of the MJO. Since the MJO major convection region is leaded by its planetary boundary layer (PBL) moisture convergence, here a frictional skeleton model is built by implementing a slab PBL into the neutral skeleton model. As a skeleton model allowing the scale interaction, this model is only valid for large-scale waves. This study shows that the PBL frictional convergence provides a strong instability source for the long eastward modes, although it also destabilizes very short westward modes. For the long waves (wavenumber less than 5), the PBL Ekman pumping moistens the low troposphere to the east of the MJO convective envelope, and sets up favorable moist conditions to destabilize the MJO and favor only eastward modes. Sensitivity experiments show that a weak PBL friction will enhance the instability slightly. The sea surface temperature (SST) with a maximum at the equator also prefers the long eastward modes. These theoretical analysis results encourage further observations on the PBL regulation of mesosynoptic-scale motions, and exploration of the interaction between PBL and multiscale motions, associated with the MJO to improve the MJO simulation in general circulation models (GCMs).