Dynamic Moisture Mode Versus Moisture Mode in MJO Dynamics: Importance of the Wave Feedback and Boundary Layer Convergence Feedback

The Madden-Julian oscillation (MJO) is an equatorial eastward moving system with an observed planetary-scale coupled Kelvin-Rossby wave structure. The equatorial waves and their interaction with convection are expected to play an important role in MJO dynamics. The moisture mode (MM) theory emphasizes the moisture thermodynamics and its interaction with convection, while it overlooks dynamic feedbacks, i.e. the wave feedback (WF) and boundary layer convergence feedback (BLCF), which are the feedbacks of the wave propagation and the BL convergence to the moisture (and the convection) field, respectively. Using the trio-interaction model for the essential MJO dynamics, this study investigates the importance of the WF and BLCF, by comparing the MM that contains only moisture feedback(MF) and cloud-radiative feedback (CRF), with the dynamic moisture mode (DMM) that includes additional WF and BLCF.

It is shown that the WF and the BLCF fundamentally change the properties of the MM. The MM has no planetary scale selection as the growth rate decreases with increasing wavelength. It has unrealistic low phase speed and low frequency at wavenumber 2-4. Meanwhile, the DMM has a planetary scale selection as the growth rate increases with increasing wavelength. The DMM has more realistic phase speed and dispersion relation at the planetary scales (wavenumber 1-3). Additionally, the horizontal structure (i.e. the ratio between the intensities of the Kelvin and Rossby wave components) is roughly fixed and independent of the propagation speed in the MM, whereas in the DMM the propagation speed is closely related to the horizontal structure. These fundamental differences between the two MJO modes lie in the WF and the BLCF.

The physical mechanisms by which the dynamic feedbacks (i.e. the WF and the BLCF) affect the MJO mode are explored. The dynamic feedbacks produce the planetary scale selection of the DMM through generating more eddy available moist static energy on the longer wavelengths. The WF can significantly change the structure of the MM and links the propagation of the DMM to the Kelvin and Rossby wave components, with stronger Kelvin (Rossby) wave favoring faster (slower) propagation. The WF also relates the dispersion feature of the DMM to the properties of the Kelvin and Rossby waves. Since the Kelvin-wave (Rossby-wave) frequency increases (decreases) with increasing wavenumber, their coupling in the DMM yields a quasi-constant frequency at the planetary scales (wavenumber 1-3). The BLCF enhances the Kelvin wave component on the longer wavelengthsthrough generating eddy available moist static energy, changing the horizontal structures, accelerating the eastward propagation and increasing the frequency to a reasonable value.