A New Multiscale Model for the Madden–Julian Oscillation

A multiscale model of the MJO is developed here that accounts, in a simplified fashion, for both the upscale transfer from synoptic to planetary scales of momentum and temperature from wave trains of thermally driven equatorial synoptic-scale circulations in a moving convective envelope as well as direct mean heating on planetary scales. This model involves idealized thermally driven congestus synoptic-scale fluctuations in the eastern part of the moving wave envelope and convective superclusters in the western part of the envelope. The model self-consistently reproduces qualitatively many of the detailed structural features of the planetary circulation in the observations of the MJO, including the vertical structure in both the westerly onset region and the strong westerly wind burst region, as well as the horizontal quadrupole planetary vortex structure. The westerly midlevel inflow in the strong westerly region and the quadrupole vortex are largely produced in the model by the upscale transport of momentum to the planetary scales, while the midlevel easterly jet in the westerly onset region is substantially strengthened by this process. The role of wave trains of tilted organized synoptic-scale circulations is crucial for this fidelity with observations. The appeal of the multiscale models developed below is their firm mathematical underpinnings, simplicity, and analytic tractability while remaining self-consistent with many of the features of the observational record.