The in-phase component of the top heaviness metric describes how top heavy organized convection is along different frequencies and wavenumbers. The quadrature component describes the tilting in vertical velocity.
The in-phase GMS describes the import of MSE to a region of convection and can be thought as acting to maintaining it or dissipating it. The quadrature component of the GMS can be thought as being responsible for the propagation of the precipitation anomalies.
The proposed method is used to elucidate several characteristics of convectively coupled waves and the MJO. It is found that convection in westward-propagating waves predominantly propagates through horizontal MSE advection. For eastward-propagating modes, it is found that Kelvin waves propagate through vertical MSE advection, while horizontal advection dominates in the MJO band. The in-phase GMS is found to be smaller for the MJO band than in the surrounding frequencies and wavenumbers. This is a result of the MJO being restricted to regions of high climatological moisture, which causes the GMS to be smaller in spite of the profile of vertical velocity being top-heavier. The critical GMS, a quantity that describes MSE sources/sinks from diabatic processes, is found to exhibit a structure reminiscent of a “red spectrum”, favoring growth at the lowest frequencies and the largest scales.