Tropical-extratropical interactions with the MJO skeleton and climatological mean flow

Simplified asymptotic models are developed to investigate tropical-extratropical interactions. Two kinds of interactions are illustrated in the model: (i) MJO initiation through extraction of energy from barotropic Rossby waves and (ii) MJO termination via energy transfer to extratropical Rossby waves. A new feature, in comparison to previous simplified models, is that here these waves interact directly in the presence of a climatological mean flow given by the Walker circulation. The simplified models are systems of ordinary differential equations (ODEs) for the amplitudes of barotropic Rossby waves and the MJO, and they are systematically derived from the MJO skeleton model by using multiscale asymptotics. The simplified ODEs allow for rapid investigation of a wide range of model parameters, such as initial conditions and wind shear. Zonally uniform wind shear is shown to have only a minor effect on these interactions here, in contrast to the important role of the zonally varying wind shear associated with the Walker circulation. The models illustrate some realistic features of tropical-extratropical interactions on intraseasonal to seasonal time scales. A key aspect of the models here is that the water vapor and convective activities are interactive components of the model, rather than specified external heating sources.