The Madden-Julian Oscillation (MJO) is the dominant component of tropical intraseasonal variability, and a theory explaining its structure and successful numerical simulation remains a major challenge. A successful model for the MJO should have a propagation speed of 4 -7 m/s predicted by theory; a wavenumber-2 or -3 structure for the planetary-scale, low-frequency envelope with distinct active and inactive phases of deep convection; an intermittent turbulent chaotic multiscale structure within the planetary envelope involving embedded westward-and eastward-propagating deep convection events; and qualitative features of the low-frequency envelope from the observational record regarding, e.g., its zonal flow structure and heating. Here, such an MJO analog is produced by using the recent multicloud model of Khouider and Majda in an appropriate intraseasonal parameter regime for flows above the equator so that rotation is ignored. Key features of the multicloud model are (i) systematic low-level moisture convergence with retained conservation of vertically integrated moist static energy, and (ii) the use of three cumulus cloud types (congestus, stratiform, and deep convective) together with their differing vertical heating structures. Besides all of the above structure in the MJO analog waves, there are accurate predictions of the phase speed from linear theory and transitions from weak, regular MJO analog waves to strong, multiscale MJO analog waves as climatological parameters vary. With all of this structure in a simplified context, these models should be useful for MJO predictability studies in a fashion akin to the Lorenz 96 model for the midlatitude atmosphere.coherent planetary intraseasonal variability ͉ multiscale structure ͉ intermittency in convection ͉ nonlinear analog model
T he dominant component of intraseasonal variability in theTropics is the 40-to 50-day tropical intraseasonal oscillation, often called the Madden-Julian Oscillation (MJO) after its discoverers (1). In the troposphere, the MJO is an equatorial planetary-scale wave envelope of complex multiscale convective processes that begins as a standing wave in the Indian Ocean and propagates across the western Pacific at a speed of Ϸ5 m⅐s Ϫ1 (2-5). The planetary-scale circulation anomalies associated with the MJO significantly affect monsoon development and intraseasonal predictability in midlatitudes and the development of the El Niño southern oscillation in the Pacific Ocean, which is one of the most important components of seasonal prediction (6, 7). Present-day computer general circulation models typically poorly represent the MJO (8, 9). One conjectured reason for the poor performance of general circulation models is the inadequate treatment across multiple spatial scales of the interaction of the hierarchy of organized structures that generate the MJO as their envelope.There have been a large number of theories attempting to explain the MJO through a specific linearized mechanism, such as evaporation-wind feedback (10, 11), boundary layer...