MODES OF TROPICAL VARIABILITY UNDER CONVECTIVE ADJUSTMENT AND THE MADDEN-JULIAN OSCILLATION .1. ANALYTICAL THEORY

The interaction between the collective effects of cumulus convection a nd large-scale dynamics is examined using the Betts-Miller moist conve ctive adjustment (MCA) parmeterization in a linearized primitive equat ion model on an equatorial beta plane. In Part I of this paper, an ana lytical approach to the eigenvalue problem is taken using perturbation expansions in the cumulus adjustment time, which is short compared to planetary dynamical time scales. The modes of tropical variability th at arise under MCA are dominated by the presence of moist processes; s ome modes act to adjust the system rapidly toward a convectively adjus ted state, while others evolve on time scales set by the large-scale d ynamics subject to near-adjusted (quasi equilibrium) thermodynamical c onstraints. Of the latter, a single vertical mode stands out, which ob eys special balances implied by the quasi-equilibrium constraints and is the only propagating deep convective mode. The propagation speed is determined by an internally defined gross moist stability. For the Ke lvin meridional mode, the phase speed and vertical structure are highl y suggestive of those of the Madden-Julian (MJ) oscillation. For the s imple case considered here, which assumes a homogeneous, separable bas ic state and sufficiently large zonal scales, the modes of variability found under MCA are all stable under reasonable conditions, although a large subclass of modes (including the MJ mode) is only slowly decay ing. This contrasts with many studies using Kuo-like convective parame terizations, which have conjectured that convective instability of the second kind (CISK) plays a role in maintaining planetary-scale tropic al variability. The authors suggest that a terminology is needed by wh ich to refer to convective interaction with dynamics (CID), without ne cessarily assuming that large-scale instability arises from this inter action. Under MCA, there is strong CID but not generally CISK. Instabi lity of the MJ mode can occur through evaporation-wind feedback. This behavior under MCA provides a suggestive prototype for tropical motion s evolving under quasi-equilibrium convective constraints.