Effects of Moisture Feedback in Frictional Coupled Kelvin-Rossby Wave Model and Implication to Madden-Julian Oscillation

The authors present an extended frictionally coupled Kelvin-Rossby wave model that includes moisture feedback to explore the role of the planetary boundary layer (BL) frictional convergence (FC) and moisture feedback (MF) in the Madden-Julian Oscillation (MJO) dynamics. This new model extends the original model of Wang and Rui (1990) by including the moisture tendency term (or 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” FC mode and ‘pure' MF mode, as well as combined FC-MF mode or dynamical moisture mode. As such, it shows that without the BL frictional moisture convergence, the MF modes are nearly stationary and damped. Not only does the BL frictional feedback make the damping MF modes grow with preferred planetary scale but it also enables the nearly stationary MF modes to move eastward slowly, resulting in an oscillation period of 30-90 days. These results suggest the critical importance of the frictional feedback in generation of eastward propagating unstable mode and selection of the preferred planetary scales. The MF process slows down the eastward-propagating short FC modes by delaying the deep convection occurrence and by enhancing the Rossby wave component. However, the longest wave (wavenumber one) is insensitive to MF and the convective adjustment time in the Betts-Miller scheme, indicating that the unstable wavenumber one FC mode is primarily controlled by the BL frictional feedback process. Implications of these theoretical results on the MJO simulation in the GCMs are discussed.