Instability and nonlinear dynamics of the MJO in a tropical channel model with vertically varying convective adjustment

In the tropical atmosphere, weather and climate are influenced by dispersive equatorial waves and their coupling with water vapor, deep convection, and rainfall. The dominant mode of variability on intraseasonal time scales is the Madden–Julian Oscillation (MJO), which is still not fully understood. Here we investigate the question: Is the MJO a linearly stable wave or an unstable wave? The linearly stable (i.e., damped) MJO regime, in which case random stochastic forcing provides the source for MJO variability, was previously investigated in a linear version of a model that has a convective adjustment parameterization. Here, to assess the other alternative, nonlinearity is added to the model and allows the study of the linearly unstable MJO regime. Model simulations are performed and evaluated for their ability to generate MJO variability as well as the full spectrum of tropical variability such as convectively coupled equatorial waves (CCEWs). In simulations of unstable growth, nonlinear advection slows the growth, and the wave saturates with reasonable amplitude, structure, speed, and dynamics. In further tests, MJO instability can sometimes excite CCEW variability, but only in a subset of cases. Overall, both the stable and unstable MJOs appear to be reasonable and may arise in different situations due to different environmental conditions.