Core Dynamics of the MJO

Abstract The Madden–Julian oscillation (MJO) is a large-scale eastward-moving system that dominates tropical subseasonal perturbations with far-reaching impacts on global weather–climate. For nearly a half century since its discovery, there has not been a consensus on the most fundamental dynamics of the MJO, despite intensive studies with a number of theories proposed. In this study, using a simple analytical approach, we found a solution to the linear equatorial shallow-water equations with momentum damping that resembles a harmonic oscillator. This solution exhibits the key characteristics of the observed MJO: its intraseasonal periodicity at the planetary scale and eastward propagation. In contrast to theories that interpret the MJO as a new mode of variability emerging from the evolution in moisture, our solution emphasizes that the core of the MJO resides in the dynamics without explicit fluctuations in moisture. Moisture still plays a role in supplying energy to the core dynamics of the MJO, and determining the value of the equivalent depth required by the theory. The energy source may come from stochastic forcing in the tropics or from the extratropics. The scale selection for the MJO comes from scale-dependent responses to scale-independent Rayleigh damping. We also demonstrate that the MJO solution introduced here reproduces the observed swallowtail structure and the phase relation between zonal wind and geopotential of the MJO, and the continuum nature of the transition between the MJO and Kelvin waves. Roles of feedback mechanisms in the MJO are also discussed using the same simple mathematical framework.