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We derive a multi-scale model of moist tropical dynamics which is valid on horizontal synoptic scales, zonal planetary scales, synoptic and intraseasonal time scales. The Intraseasonal Multi-Scale Moist Dynamics (IMMD) framework builds on the IPESD framework of (Majda and Klein 2003). It generalizes the latter by allowing for strong zonal winds (the Trade Winds) and the pressure and stratification variations that they generate. The framework consists of three pieces. The first, called TH, are planetary scale climatology modulation equations which govern the Trade Winds and Hadley Circulation. The second, S, are a linear system of equations which govern the synoptic scale fluctuations and forced by synoptic scale heating fluctuations. Unlike the IPESD theory, these fluctuations are advected by the zonal component of the Trade Winds however, not by the meridional components of the Hadley Circulation. The third, P, govern the planetary scale anomalies and, like IPESD, are driven both by planetary scale mean heating and by upscale fluxes from the synoptic scales. These planetary scale anomalies are advected, both, by the zonal component of the Trade Winds and by the meridional component of the Hadley Circulation and, furthermore, respond to an in-scale flux from the mean climatology. We also present an asymptotic analysis of the equations of bulk cloud thermodynamics in order to lay out a self-contained path for incorporating synoptic scale cloud models into the IMMD framework. This framework has potentially important implications for the development of models describing the Madden-Julian Oscillation (MJO) since the MJO manifests itself as planetary scale anomalies from a mean climatology which it modulates on intraseasonal time scales.

Intraseasonal multi-scale moist dynamics of the tropical atmosphere