Effects of moisture feedback in a frictional coupled Kelvin–Rossby wave model and implication in the Madden–Julian oscillation dynamics

The authors extend the original frictional wave dynamics and implement the moisture feedback (MF) to explore the effects of planetary boundary layer (PBL) process and the MF on the Madden–Julian Oscillation (MJO). This new system develops the original frictional wave dynamics by including the moisture tendency term (or the MF mode), along with a parameterized precipitation based on the Betts–Miller scheme. The linear instability analysis of this model provides solutions to elucidate the behaviors of the “pure” frictional convergence (FC) mode and the “pure” MF mode, respectively, as well as the behaviors of the combined FC–MF mode or the dynamical moisture mode. These results show that without the PBL frictional moisture convergence, the MF mode is nearly stationary and damped. Not only does the PBL frictional feedback make the damping MF mode grow with preferred planetary scale but it also enables the nearly stationary MF mode to move eastward slowly, resulting in an oscillation with a period of 30–90 days. This finding suggests the important role of the frictional feedback in generating eastward propagating unstable modes and selecting the preferred planetary scales. The MF process slows down the eastward-propagating short-wave FC mode by delaying the occurrence of deep convection and by enhancing the Rossby wave component. However, the longest wave (wavenumber one) is insensitive to the MF or the convective adjustment time, indicating that the unstable longest wave is primarily controlled by PBL frictional feedback process. Implications of these theoretical results in MJO simulation in general circulation models are discussed.