Reexamination of the Wave Activity Envelope Convective Scheme in Theoretical Modeling of MJO

Abstract The skeleton model is one of the theoretical models for understanding the essence of the Madden–Julian oscillation (MJO). The heating parameterization scheme in the skeleton model assumes that precipitation tendency is in phase and proportional to the low-level moisture anomaly. The authors show that the observed MJO precipitation tendency is not in phase with the low-level moisture anomaly. The consequence of the wave activity envelope (WAE) scheme is reexamined by using a general MJO theoretical framework in which trio-interaction among convective heating, moisture, and wave–boundary layer (BL) dynamics are included and various simplified convective schemes can be accommodated. Without the BL dynamics, the general model framework can be reduced to the original skeleton model. The authors show that the original skeleton model yields a neutral mode that exhibits a “quadrupole” horizontal structure and a quadrature relationship between precipitation and low-level moisture; both are inconsistent with observations. With the BL dynamics and damping included, the model can produce a growing mode with improved horizontal structure and precipitation–moisture relationship, but deficiencies remain because of the WAE scheme. The authors further demonstrate that the general model with the simplified Betts–Miller scheme and BL dynamics can produce a realistic horizontal structure (coupled Kelvin–Rossby wave structure) and precipitation–moisture relationship (i.e., the BL moisture convergence leads precipitation, and column-integrated moisture coincides with precipitation).