Modes of Tropical Variability under Convective Adjustment and the Madden–Julian Oscillation. Part II: Numerical Results

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Abstract
Convective interaction with dynamics (CID) dictates the structure and behavior of the eigenmodes of the tropical atmosphere under moist convective adjustment (MCA) when the convective adjustment time scale, τc, is much smaller than dynamical time scales, as examined analytically in Part I. Here, the modes are reexamined numerically to include the effects of finite τc, again for a primitive equation model with the Betts-Miller MCA parameterization. The numerical results at planetary scales are consistent with the analytical approach, with two well-separated classes of vertical modes: one subset evolves at the cumulus time scale, while the other subset evolves at a time scale set by the large-scale dynamics. All modes are stable for homogeneous basic states in the presence of simple mechanical damping effects. Thus, there is no CISK at any scale under MCA. However, the finite τc effect has the property of selectively damping the smallest scales while certain vertical modes at planetary scales decay only slowly. This planetary scale selection contrasts to many linear CISK studies, which tend to select the smallest scale. The Madden–Julian mode, which resembles the observed tropical intraseasonal oscillation, is found as a single vertical mode arising through Kelvin wave-CID. When the evaporation-wind feedback is included, this slowly decaying MJ mode is selectively destabilized at wavenumber one or two, consistent with the observations in the tropics. Stochastic forcing by nonresolved mesoscale processes can also potentially account for the existence of large-scale tropical variance. When the stochastic forcing occurs in the thermodynamic equation, the propagating deep-convective mode at planetary scales is the most strongly excited. Kinematic forcing excites slowly decaying kinematically dominated modes but cannot account for the characteristics of observed Madden-Julian variance.

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