Role of delayed deep convection in the Madden-Julian oscillation

Abstract

The power spectrum of Madden-Julian oscillation (MJO) has a peculiar dispersion relation and is well separated from the convectively coupled equatorial waves (CCEWs). The authors present a theoretical model coupling the equatorial Rossby and Kelvin waves to understand this spectral feature of MJO. In this model, a delay process for triggering the deep convection from the additional planetary boundary layer (PBL) pumped moisture is implemented. This model has a moist Kelvin wave-like dispersion relation, and short waves grow fast when all moisture pumped by the PBL excites the deep convection instantly. When the moisture pumped by the PBL is delayed to stay in the lower troposphere for a time scale on the order of a day before triggering the deep convection, this model simulates a MJO-like mode, for which three features of the MJO, the peculiar dispersion relation, the horizontal quadrupole-vortex structure, and longest waves having maximum growth rate, have been simulated. Both moist Kelvin wave-like mode and MJO-like mode are simulated simultaneously when part of the deep convection is delayed, where the strong instability occurs at low-frequency long wavelength for the MJO-like mode and at high-frequency short wavelength for the moist Kelvin wave-like mode. These results suggest the importance of the delay process of deep convection in simulating the MJO.