Exploring Solutions of Simple Linear Models of the Madden-Julian Oscillation

Models of the Madden-Julian Oscillation (MJO) exist at varying levels of complexity. Simple linear models attempt to explain the MJO’s near-planetary scale and slow eastward propagation using linearized equations of motion with key physical processes represented by several parameters. These parameters, while often estimated from observational data, are generally taken as constants in the model. Despite this, previous research suggests that many parameters have both spatial-scale and latitude-longitude dependencies. Neglecting these dependencies simplifies the model but complicates the relationship between model-derived MJO-like modes and the observed MJO.

This study expands upon the model presented in Ahmed (2021) to examine the sensitivity of the model solution – an MJO-like mode – to model parameters such as convective sensitivity to moisture and temperature anomalies and the coefficients that relate anomalous winds to horizontal moisture gradients. We solve both analytic and numerical representations of a modified Ahmed (2021) model to explore the parameter dependency. We find that simple modifications to the assumed symmetric meridional distribution of mean-state moisture allow the model to capture the asymmetric behavior of the observed MJO about the equator. Additionally, we find that the group velocity, phase speed, and growth rate of the MJO-like mode strongly depend on both the relative magnitudes of convective moisture and temperature sensitivity, as well as the degree to which Weak Temperature Gradient (WTG) balance is assumed.