Analysis of a simple Madden–Julian Oscillation model using a moisture variable with memory

Abstract The Madden–Julian oscillation (MJO) is a significant source of intraseasonal rainfall and variability in the Tropics. Accurate modeling of the MJO remains a challenge due to its multiscale nature. Simple models of the MJO help explain the mechanisms in play, but currently there are many such models with diverse mechanisms and properties. These models often start with a dry dynamical core on an equatorial beta‐plane coupled with moisture. However, to achieve a realistic MJO mode, some of these models contain an extra prognostic equation (e.g., for convective amplitude, stratified moisture, or boundary‐layer winds) but others do not. We show that simple convective adjustment of moisture produces a slow eastward mode that resembles the MJO but decays rapidly. To persist the MJO to longer time‐scales, two primary mechanisms can be incorporated: (a) feedback mechanisms where precipitation is directly influenced by dry variables, or (b) an additional prognostic “memory” variable that feeds back to both moisture and dry variables. Both mechanisms can give realistic frequency and decay rates, but an additional prognostic variable leads to a horizontal structure along the Equator with reduced temperature perturbations and moisture leading convergence anomalies. Thus, the memory variable gives a more detailed structure to an MJO model. Additionally, the memory variable yields a slow westward “memory mode”. Finally, we show that the additional variable in at least one idealized model can be directly related to “convective memory” found in detailed process studies.