Multi-cloud models for the MJO

The lecture surveys recent theoretical progress in understanding the multi-scale features of the MJO in idealized settings. Recent observational analysis reveals the central role of three multicloud types, congestus, stratiform, and deep convective cumulus clouds, in the dynamics of large-scale convectively coupled Kelvin waves, westward-propagating two-day waves, and the Madden–Julian oscillation. Systematic model convective parameterizations highlighting the dynamic role of the three cloud types have been developed recently (Khouider and Majda, JAS, 2006, 2007; JAS in press 2007) through two baroclinic modes of vertical structure: a deep convective heating mode and a second mode with low-level heating and cooling corresponding respectively to congestus and stratiform clouds. A systematic moisture equation is developed where the lower troposphere moisture increases through detrainment of shallow cumulus clouds, evaporation of stratiform rain, and moisture convergence and decreases through deep

convective precipitation. A nonlinear switch is developed that favors either deep or congestus convection depending on the relative dryness of the troposphere; in particular, a dry troposphere with large convective available potential energy (CAPE) has no deep convection and only congestus clouds.

There are several new results surveyed here using the multi-cloud models directly in the idealized setting of flows above the equator without rotation to produce “MJO-like” multi-scale wave patterns with several key features of the MJO (Khouider and Majda, JAS 2007; JAS in press 2007; Majda, Stechmann, Khouider, PNAS 2007). The multi-cloud models do not have WISHE, radiative instability, boundary layer frictional convergence, or convective momentum transport yet have multi-scale packets of convectively coupled waves moving in one direction at 15/20 m/s with their large scale envelopes moving in the opposite direction at speeds of 4 to 7 m/s, reminiscent of the MJO. The large scale envelopes resemble the zonal structure of the MJO but the westerly wind burst is too weak, probably due to the absence of upscale momentum fluxes. Current research includes blending the two different theories with earlier work (Majda and Biello, PNAS 2004; Biello and Majda, JAS 2005, DAO 2006) to incorporate convective momentum transport in the multi-cloud models and including the crucial feature of rotation on equatorial beta plane.

All these papers are available on Andrew Majda's NYU faculty website: http://math.nyu.edu/faculty/majda/index.html