Haertel P. T., G. Kiladis, A. Denno and T. M. Rickenbach (March 2008): Vertical-Mode Decompositions of 2-Day Waves and the Madden–Julian Oscillation. J. Atmos. Sci., 65 (3), 813-833. doi:10.1175/2007JAS2314.1Full text not available from this repository.
Vertical structures of 2-day waves and the Madden–Julian oscillation (MJO) are projected onto vertical normal modes for a quiescent tropical troposphere. Three modes capture the gross tropospheric structure of 2-day waves, while only two modes are needed to represent most of the baroclinic structure of the MJO. Deep circulations that project onto the first baroclinic mode are associated with deep cumulonimbus and stratiform rainfall. Shallow circulations that project onto higher wavenumber modes are associated with precipitating shallow cumulus and congestus and stratiform rainfall. For both disturbances the horizontal divergence contributed by shallow modes is an important factor in the column-integrated moist enthalpy budget. These modes converge moist static energy for a time prior to when deep circulations export moist static energy. These results highlight the importance of properly representing the effects of shallow cumulus, congestus, and stratiform precipitation in theories of convectively coupled waves and in atmospheric models.
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