Normal mode interactions in the Madden Julian Oscillation envelope

The Madden Julian Oscillation (MJO) is the dominant element of the atmospheric variability  in the tropics on intraseasonal zonal timescales. The MJO manifests itself as a slowly eastward propagating envelope coupling large scale circulation and convection. Despite recent progress in the understanding of the MJO, a comprehensive theory of the MJO is still missing, partly due to its complexity associated with moist physics and nonlinearity.
Here, we use a normal mode decomposition of atmospheric reanalysis datasets to show that the MJO can be understood in terms of a superposition of interacting Rossby, Kelvin  and inertio-gravity modes. We discuss the nature of the interaction between these modes, which can be either linear, due to large-scale variations in the moisture, or simply due to the inherent nonlinearity of the equations of the atmosphere.