Andrew J. Majda* and Joseph Biello Department of Mathematics and Climate, Atmosphere, Ocean Science (CAOS) Courant Institute New York University
* Talk presented by A. Majda
The dominant component of intraseasonal variability in the tropics is the 40-50 day tropical intraseasonal oscillation, often called the Madden-Julian oscillation (MJO) after its discoverers (Madden & Julian (1972)). In the troposphere, the MJO is an equatorial planetary scale wave envelope of complex multi-scale convective processes which propagates across the Indian Ocean and Western Pacific at a speed of roughly 5 ms-1 (Nakazawa (1988), Hendon & Salby (1994), Hendon & Liebmann (1994), Maloney & Hartmann (1998)). The planetary scale circulation anomalies associated with the MJO significantly affect monsoon development, intraseasonal predictability in mid-latitudes, and impact the development of the El Nino Southern Oscillation (ENSO) in the Pacific Ocean (Madden & Julian (1994), Vecchi (2000), Zhang & Anderson (2003). Present day computer general circulation models (GCM) typically poorly represent the MJO (Sperber et al. (1997)). One conjecture for the reason for this poor performance of GCM's is the inadequate treatment across multiple spatial scales of the interaction of the hierarchy of organized structures which generate the MJO as their envelope.
A multi-scale model of the MJO is developed here (Majda & Biello, PNAS, 2004; Biello & Majda, JAS, 2005) which 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 warm pool anomaly 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 superconvective clusters 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 multi-scale 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.
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